G. B. Alalykin, S. K. Godunov, L. L. Kireyeva, and L. A. Pliner, Solution of One- Dimensional Problems in Gas Dynamics on Moving Grids, 1970.

J. S. Antunes-do-carmo, F. J. Santos, and E. Barthélemy, Surface waves propagation in shallow water: A finite element model, International Journal for Numerical Methods in Fluids, vol.6, issue.6, pp.447-459, 1993.
DOI : 10.1002/fld.1650160602

C. Arvanitis and A. I. Delis, Behavior of Finite Volume Schemes for Hyperbolic Conservation Laws on Adaptive Redistributed Spatial Grids, SIAM Journal on Scientific Computing, vol.28, issue.5, pp.1927-1956, 2006.
DOI : 10.1137/050632853

C. Arvanitis, T. Katsaounis, and C. Makridakis, Adaptive Finite Element Relaxation Schemes for Hyperbolic Conservation Laws, ESAIM: Mathematical Modelling and Numerical Analysis, vol.35, issue.1, pp.17-33, 2010.
DOI : 10.1051/m2an:2001105

S. Assier-rzadkieaicz, P. Heinrich, P. C. Sabatier, B. Savoye, and J. F. Bourillet, Numerical Modelling of a Landslide-generated Tsunami: The 1979 Nice Event, Pure and Applied Geophysics, vol.157, issue.10, pp.1707-1727, 2000.
DOI : 10.1007/PL00001057

B. N. Azarenok, S. A. Ivanenko, and T. Tang, Adaptive Mesh Redistibution Method Based on Godunov's Scheme, Communications in Mathematical Sciences, vol.1, issue.1, pp.152-179, 2003.
DOI : 10.4310/CMS.2003.v1.n1.a10

N. S. Bakhvalov, The optimization of methods of solving boundary value problems with a boundary layer, USSR Computational Mathematics and Mathematical Physics, vol.9, issue.4, pp.139-166, 1969.
DOI : 10.1016/0041-5553(69)90038-X

V. B. Barakhnin and G. S. Khakimzyanov, On the algorithm for one nonlinear dispersive shallow-water model, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.12, issue.4, pp.293-317, 1997.
DOI : 10.1515/rnam.1997.12.4.293

V. B. Barakhnin and G. S. Khakimzyanov, The splitting technique as applied to the solution of the nonlinear dispersive shallow-water equations, Doklady Mathematics, vol.59, issue.6, pp.70-72, 1999.

T. J. Barth and M. Ohlberger, Finite Volume Methods: Foundation and Analysis, Encyclopedia of Computational Mechanics, p.22, 2004.
DOI : 10.1090/trans2/026/05

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.6.403

E. Barthélémy, Nonlinear shallow water theories for coastal waves, pp.315-337, 2004.

S. A. Beisel, L. B. Chubarov, D. Dutykh, G. S. Khakimzyanov, and N. Y. Shokina, Simulation of surface waves generated by an underwater landslide in a bounded reservoir, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.27, issue.6, pp.539-558
DOI : 10.1515/rnam-2012-0031

S. A. Beisel, L. B. Chubarov, and G. S. Khakimzyanov, Simulation of surface waves generated by an underwater landslide moving over an uneven slope, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.26, issue.1, pp.17-38, 2011.
DOI : 10.1515/rjnamm.2011.002

T. B. Benjamin, J. L. Bona, and J. J. Mahony, Model Equations for Long Waves in Nonlinear Dispersive Systems, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.272, issue.1220, pp.47-78, 1972.
DOI : 10.1098/rsta.1972.0032

M. J. Berger, D. L. George, R. J. Leveque, and K. T. Mandli, The GeoClaw software for depth-averaged flows with adaptive refinement, Advances in Water Resources, vol.34, issue.9, pp.1195-1206
DOI : 10.1016/j.advwatres.2011.02.016

N. Bohr, Über die Serienspektra der Element, Zeitschrift für Physik, pp.423-469
DOI : 10.1007/bf01329978

J. L. Bona, V. A. Dougalis, and O. A. Karakashian, Fully discrete galerkin methods for the korteweg-de vries equation, Computers & Mathematics with Applications, vol.12, issue.7, pp.859-884, 1986.
DOI : 10.1016/0898-1221(86)90031-3

URL : http://doi.org/10.1016/0898-1221(86)90031-3

P. Bonneton, F. Chazel, D. Lannes, F. Marche, and M. Tissier, A splitting approach for the fully nonlinear and weakly dispersive Green???Naghdi model, Journal of Computational Physics, vol.230, issue.4, pp.1479-1498, 2011.
DOI : 10.1016/j.jcp.2010.11.015

URL : https://hal.archives-ouvertes.fr/hal-00482564

M. Bristeau, N. Goutal, and J. Sainte-marie, Numerical simulations of a non-hydrostatic shallow water model, Computers & Fluids, vol.47, issue.1, pp.51-64, 2011.
DOI : 10.1016/j.compfluid.2011.02.013

URL : https://hal.archives-ouvertes.fr/hal-00654634

M. Brocchini, A reasoned overview on Boussinesq-type models: the interplay between physics, mathematics and numerics, Proc. R. Soc. A, p.46920130496, 2005.
DOI : 10.1007/s10652-012-9252-5

J. G. Byatt-smith, The reflection of a solitary wave by a vertical wall, Journal of Fluid Mechanics, vol.15, issue.-1, pp.503-521, 1988.
DOI : 10.1017/S0022112077000081

F. Carbone, D. Dutykh, J. M. Dudley, and F. Dias, Extreme wave runup on a vertical cliff, Geophysical Research Letters, vol.15, issue.6, pp.3138-3143, 2013.
DOI : 10.1103/PhysRevLett.15.240

URL : https://hal.archives-ouvertes.fr/hal-00905964

M. J. Castro, M. De-la-asuncion, J. Macias, C. Parés, E. D. Fernandez-nieto et al., IFCP Riemann solver, Numerical Methods for Hyperbolic Equations: Theory and Applications, pp.237-244, 2013.
DOI : 10.1201/b14172-32

V. Casulli, A semi-implicit finite difference method for non-hydrostatic, free-surface flows, International Journal for Numerical Methods in Fluids, vol.23, issue.4, pp.425-440, 1999.
DOI : 10.1029/CO004p0001

J. Chambarel, C. Kharif, and J. Touboul, Head-on collision of two solitary waves and residual falling jet formation, Nonlinear Processes in Geophysics, vol.16, issue.1, pp.111-122, 2009.
DOI : 10.5194/npg-16-111-2009

URL : https://hal.archives-ouvertes.fr/hal-00442167

R. K. Chan and R. L. Street, A computer study of finite-amplitude water waves, Journal of Computational Physics, vol.6, issue.1, pp.68-94, 1970.
DOI : 10.1016/0021-9991(70)90005-7

K. Chang, T. Hsu, and P. L. Liu, Vortex generation and evolution in water waves propagating over a submerged rectangular obstacle, Coastal Engineering, vol.44, issue.1, pp.13-36, 2001.
DOI : 10.1016/S0378-3839(01)00019-9

J. G. Charney, R. Fjörtoft, and J. Neumann, Numerical Integration of the Barotropic Vorticity Equation, Tellus, vol.2, issue.29, pp.237-254, 1950.

F. Chazel, D. Lannes, and F. Marche, Numerical Simulation of Strongly Nonlinear and Dispersive Waves Using a Green???Naghdi Model, Journal of Scientific Computing, vol.37, issue.3, pp.105-116, 2011.
DOI : 10.1002/fld.186

URL : https://hal.archives-ouvertes.fr/hal-00482561

J. Chen, M. Qin, and Y. Tang, Symplectic and multi-symplectic methods for the nonlinear Schrödinger equation, Computers & Mathematics with Applications, vol.43, pp.8-91095, 1957.

M. Chhay, D. Dutykh, and D. Clamond, On the multi-symplectic structure of the Serre???Green???Naghdi equations, Journal of Physics A: Mathematical and Theoretical, vol.49, issue.3, pp.3-4, 1957.
DOI : 10.1088/1751-8113/49/3/03LT01

URL : https://hal.archives-ouvertes.fr/hal-01221356

A. Chorin, Numerical solution of the Navier-Stokes equations, Mathematics of Computation, vol.22, issue.104, pp.745-762, 1968.
DOI : 10.1090/S0025-5718-1968-0242392-2

L. B. Chubarov, S. V. Eletsky, Z. I. Fedotova, and G. S. Khakimzyanov, Simulation of surface waves generation by an underwater landslide, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.18, issue.2, pp.425-437, 2005.
DOI : 10.1023/A:1007934804464

L. B. Chubarov, Z. I. Fedotova, Y. I. Shokin, and B. G. Einarsson, Comparative Analysis of Nonlinear Dispersive Shallow Water Models, International Journal of Computational Fluid Dynamics, vol.293, issue.1, pp.55-73, 2000.
DOI : 10.1017/S0022112087000594

L. B. Chubarov and Y. I. Shokin, The numerical modelling of long wave propagation in the framework of non-linear dispersion models, Computers & Fluids, vol.15, issue.3, pp.229-249, 1987.
DOI : 10.1016/0045-7930(87)90008-9

R. Cienfuegos, E. Barthélemy, and P. Bonneton, A fourth-order compact finite volume scheme for fully nonlinear and weakly dispersive Boussinesq-type equations. Part II: boundary conditions and validation, International Journal for Numerical Methods in Fluids, vol.51, issue.9, pp.1423-1455, 2007.
DOI : 10.1098/rspa.2004.1305

URL : https://hal.archives-ouvertes.fr/hal-00182841

D. Clamond and D. Dutykh, Practical use of variational principles for modeling water waves, Physica D: Nonlinear Phenomena, vol.241, issue.1, pp.25-36, 2012.
DOI : 10.1016/j.physd.2011.09.015

URL : https://hal.archives-ouvertes.fr/hal-00456891

M. J. Cooker, P. D. Weidman, and D. S. Bale, Reflection of a high-amplitude solitary wave at a vertical wall, Journal of Fluid Mechanics, vol.342, issue.39, pp.141-158, 1997.
DOI : 10.1017/S002211209700551X

R. Courant, K. Friedrichs, and H. Lewy, ???ber die partiellen Differenzengleichungen der mathematischen Physik, Mathematische Annalen, vol.98, issue.6, pp.32-74, 1928.
DOI : 10.1002/zamm.19260060408

M. H. Dao and P. Tkalich, Tsunami propagation modelling – a sensitivity study, Natural Hazards and Earth System Science, vol.7, issue.6, pp.741-754, 2007.
DOI : 10.5194/nhess-7-741-2007

V. H. Davletshin, Force action of solitary waves on vertical structures, Tsunami meeting, pp.41-43, 1984.

A. J. De-saint-venant, Théorie du mouvement non-permanent des eaux, avec application aux crues des rivières et à l'introduction des marées dans leur lit, C. R. Acad. Sc. Paris, vol.73, issue.8 9, pp.147-154

M. W. Dingemans, Water wave propagation over uneven bottom, World Scientific, p.40, 1997.
DOI : 10.1142/9789812796042

URL : http://repository.tudelft.nl/islandora/object/uuid%3A67580088-62af-4c6f-b32e-b3940584e5d2/datastream/OBJ/view

V. A. Dougalis and O. A. Karakashian, On some high-order accurate fully discrete Galerkin methods for the Korteweg-de Vries equation, Mathematics of Computation, vol.45, issue.172, p.45329, 1985.
DOI : 10.1090/S0025-5718-1985-0804927-8

V. A. Dougalis and D. E. Mitsotakis, Theory and Numerical Analysis of Boussinesq Systems, Effective Computational Methods in Wave Propagation, pp.63-110, 2008.
DOI : 10.1201/9781420010879.ch3

URL : https://hal.archives-ouvertes.fr/hal-00407927

V. A. Dougalis, D. E. Mitsotakis, and J. Saut, On some Boussinesq systems in two space dimensions: theory and numerical analysis, ESAIM: Mathematical Modelling and Numerical Analysis, vol.41, issue.5, pp.254-825, 2007.
DOI : 10.1051/m2an:2007043

P. G. Drazin and R. S. Johnson, Solitons: An introduction, p.45, 1989.
DOI : 10.1017/CBO9781139172059

A. Duran, D. Dutykh, and D. Mitsotakis, On the Galilean Invariance of Some Nonlinear Dispersive Wave Equations, Studies in Applied Mathematics, vol.30, issue.5, pp.359-388, 2013.
DOI : 10.1016/j.apnum.2009.03.002

D. Dutykh, M. Chhay, and F. Fedele, Geometric numerical schemes for the KdV equation, Computational Mathematics and Mathematical Physics, vol.53, issue.2, pp.221-236, 2013.
DOI : 10.1134/S0965542513020103

URL : https://hal.archives-ouvertes.fr/hal-00694896

D. Dutykh and D. Clamond, Efficient computation of steady solitary gravity waves, Wave Motion, vol.51, issue.1, pp.86-99, 1945.
DOI : 10.1016/j.wavemoti.2013.06.007

URL : https://hal.archives-ouvertes.fr/hal-00786077

D. Dutykh, D. Clamond, P. Milewski, and D. Mitsotakis, Finite volume and pseudo-spectral schemes for the fully nonlinear 1D Serre equations, European Journal of Applied Mathematics, vol.9, issue.05, pp.761-787, 2013.
DOI : 10.1017/S0022112065000745

URL : https://hal.archives-ouvertes.fr/hal-00587994

D. Dutykh and F. Dias, Dissipative Boussinesq equations, Comptes Rendus M??canique, vol.335, issue.9-10, pp.559-583, 2007.
DOI : 10.1016/j.crme.2007.08.003

URL : https://hal.archives-ouvertes.fr/hal-00137633

D. Dutykh and F. Dias, Energy of tsunami waves generated by bottom motion, Proc. R. Soc. A, pp.725-744, 2009.
DOI : 10.1017/S0022112089002089

URL : https://hal.archives-ouvertes.fr/hal-00311752

D. Dutykh and D. Ionescu-kruse, Travelling wave solutions for some two-component shallow water models, Journal of Differential Equations, vol.261, issue.2, pp.1099-1114, 2015.
DOI : 10.1016/j.jde.2016.03.035

URL : https://hal.archives-ouvertes.fr/hal-01294603

D. Dutykh and H. Kalisch, Boussinesq modeling of surface waves due to underwater landslides, Nonlinear Processes in Geophysics, vol.20, issue.3, pp.267-285, 2013.
DOI : 10.5194/npg-20-267-2013

URL : https://hal.archives-ouvertes.fr/hal-00654386

D. Dutykh, T. Katsaounis, and D. Mitsotakis, Finite volume schemes for dispersive wave propagation and runup, Journal of Computational Physics, vol.230, issue.8, pp.3035-3061, 2011.
DOI : 10.1016/j.jcp.2011.01.003

URL : https://hal.archives-ouvertes.fr/hal-00472431

D. Dutykh, T. Katsaounis, and D. Mitsotakis, Finite volume methods for unidirectional dispersive wave models, International Journal for Numerical Methods in Fluids, vol.459, issue.6, pp.717-736, 2013.
DOI : 10.1098/rspa.2002.1067

URL : https://hal.archives-ouvertes.fr/hal-00538043

D. Dutykh, D. Mitsotakis, S. A. Beisel, and N. Y. Shokina, Dispersive waves generated by an underwater landslide, Numerical Methods for Hyperbolic Equations: Theory and Applications, pp.245-250, 2013.
DOI : 10.1201/b14172-33

URL : https://hal.archives-ouvertes.fr/hal-00637102

F. Enet and S. T. Grilli, Experimental Study of Tsunami Generation by Three-Dimensional Rigid Underwater Landslides, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.133, issue.6, pp.442-454, 2007.
DOI : 10.1061/(ASCE)0733-950X(2007)133:6(442)

R. C. Ertekin, W. C. Webster, and J. V. Wehausen, Waves caused by a moving disturbance in a shallow channel of finite width, Journal of Fluid Mechanics, vol.9, issue.-1, pp.275-292, 1986.
DOI : 10.1098/rspa.1974.0072

M. S. Fabien, Spectral Methods for Partial Dierential Equations that Model Shallow Water Wave Phenomena. Master, 2014.

Z. I. Fedotova and E. D. Karepova, Variational principle for approximate models of wave hydrodynamics, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.11, issue.3, pp.183-204, 1996.
DOI : 10.1515/rnam.1996.11.3.183

Z. I. Fedotova and G. S. Khakimzyanov, Shallow water equations on a movable bottom, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.24, issue.1, pp.31-42, 2009.
DOI : 10.1515/RJNAMM.2009.003

Z. I. Fedotova, G. S. Khakimzyanov, and D. Dutykh, Abstract, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.29, issue.3, pp.167-178, 1948.
DOI : 10.1515/rnam-2014-0013

Z. I. Fedotova and V. Y. Pashkova, Methods of construction and the analysis of difference schemes for nonlinear dispersive models of wave hydrodynamics, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.12, issue.2, p.42, 1997.
DOI : 10.1515/rnam.1997.12.2.127

J. D. Fenton and M. M. Rienecker, A Fourier method for solving nonlinear water-wave problems: application to solitary-wave interactions, Journal of Fluid Mechanics, vol.350, issue.-1, pp.411-443, 1982.
DOI : 10.1016/0021-9991(70)90005-7

E. D. Fernandez-nieto, F. Bouchut, D. Bresch, M. J. Castro-diaz, and A. Mangeney, A new Savage???Hutter type model for submarine avalanches and generated tsunami, Journal of Computational Physics, vol.227, issue.16, pp.7720-7754, 2008.
DOI : 10.1016/j.jcp.2008.04.039

URL : https://hal.archives-ouvertes.fr/hal-00385939

S. Glimsdal, G. K. Pedersen, K. Atakan, C. B. Harbitz, H. P. Langtangen et al., Propagation of the Dec Indian Ocean Tsunami: Effects of Dispersion and Source Characteristics, Int. J. Fluid Mech. Res, vol.26, issue.331, pp.15-43, 2004.

S. Glimsdal, G. K. Pedersen, C. B. Harbitz, and F. Løvholt, Dispersion of tsunamis: does it really matter? Natural Hazards and Earth System Science, pp.1507-1526, 2013.

A. E. Green, N. Laws, and P. M. Naghdi, On the Theory of Water Waves, Proc. R. Soc. Lond. A, pp.43-55, 1974.
DOI : 10.1098/rspa.1974.0072

S. Grilli, S. Vogelmann, and P. Watts, Development of a 3D numerical wave tank for modeling tsunami generation by underwater landslides, Engineering Analysis with Boundary Elements, vol.26, issue.4, pp.301-313, 2002.
DOI : 10.1016/S0955-7997(01)00113-8

S. T. Grilli and P. Watts, Tsunami Generation by Submarine Mass Failure. I: Modeling, Experimental Validation, and Sensitivity Analyses, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.131, issue.6, pp.283-331, 2005.
DOI : 10.1061/(ASCE)0733-950X(2005)131:6(283)

J. Grue, E. N. Pelinovsky, D. Fructus, T. Talipova, and C. Kharif, Formation of undular bores and solitary waves in the Strait of Malacca caused by the 26 December 2004 Indian Ocean tsunami, Journal of Geophysical Research, vol.402, issue.4, pp.5008-5039, 2004.
DOI : 10.1007/978-94-010-0205-9

E. Hairer, S. P. Nørsett, and G. Wanner, Solving ordinary differential equations: Nonstiff problems, 2009.
DOI : 10.1007/978-3-662-12607-3

E. Hairer and G. Wanner, Solving Ordinary Differential Equations II. Stiff and Differential- Algebraic Problems, 1996.
DOI : 10.1007/978-3-662-09947-6

J. Hammack, D. Henderson, P. Guyenne, and M. Yi, SOLITARY-WAVE COLLISIONS, Advances in Engineering Mechanics ??? Reflections and Outlooks, p.43, 2004.
DOI : 10.1142/9789812702128_0013

F. H. Harlow and J. E. Welch, Numerical Calculation of Time-Dependent Viscous Incompressible Flow of Fluid with Free Surface, Physics of Fluids, vol.149, issue.12, p.2182, 1965.
DOI : 10.1098/rsta.1952.0006

H. Hermes, Introduction to Mathematical Logic. Universitext, p.26, 1973.

N. J. Higham, Accuracy and Stability of Numerical Algorithms, SIAM Philadelphia, p.25, 2002.
DOI : 10.1137/1.9780898718027

J. Horrillo, Z. Kowalik, and Y. Shigihara, Wave Dispersion Study in the Indian Ocean-Tsunami of December 26, 2004, Marine Geodesy, vol.120, issue.3, pp.149-166, 2004.
DOI : 10.1061/(ASCE)0733-950X(1995)121:5(251)

W. Huang, Practical Aspects of Formulation and Solution of Moving Mesh Partial Differential Equations, Journal of Computational Physics, vol.171, issue.2, pp.753-775, 2001.
DOI : 10.1006/jcph.2001.6809

W. Huang and R. D. Russell, Adaptive mesh movement ??? the MMPDE approach and its applications, Journal of Computational and Applied Mathematics, vol.128, issue.1-2, pp.383-398, 2001.
DOI : 10.1016/S0377-0427(00)00520-3

URL : http://doi.org/10.1016/s0377-0427(00)00520-3

M. Ioualalen, S. Migeon, and O. Sardoux, Landslide tsunami vulnerability in the Ligurian Sea: case study of the 1979 October 16 Nice international airport submarine landslide and of identified geological mass failures, Geophysical Journal International, vol.181, issue.48, pp.724-740, 2010.
DOI : 10.1111/j.1365-246X.2010.04572.x

URL : https://hal.archives-ouvertes.fr/hal-00468916

R. S. Johnson, Camassa???Holm, Korteweg???de Vries and related models for water waves, Journal of Fluid Mechanics, vol.455, pp.63-82, 2002.
DOI : 10.1017/S0022112001007224

A. Kabbaj, Contribution à l'étude du passage des ondes de gravité et de la génération des ondes internes sur un talus, p.44, 1985.

M. Kazolea and A. I. Delis, A well-balanced shock-capturing hybrid finite volume???finite difference numerical scheme for extended 1D Boussinesq models, Applied Numerical Mathematics, vol.67, issue.6, pp.167-186, 2013.
DOI : 10.1016/j.apnum.2011.07.003

G. Khakimzyanov and D. Dutykh, On supraconvergence phenomenon for second order centered finite differences on non-uniform grids, Journal of Computational and Applied Mathematics, vol.326, issue.16, pp.1-14, 2017.
DOI : 10.1016/j.cam.2017.05.006

URL : https://hal.archives-ouvertes.fr/hal-01223522

G. S. Khakimzyanov, D. Dutykh, and Z. I. Fedotova, Dispersive shallow water wave modelling . Part III: Model derivation on a globally spherical geometry, pp.1-40, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01547833

G. S. Khakimzyanov, D. Dutykh, Z. I. Fedotova, and D. E. Mitsotakis, Dispersive shallow water wave modelling. Part I: Model derivation on a globally flat space, pp.1-40, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01547833

G. S. Khakimzyanov, D. Dutykh, and O. Gusev, Dispersive shallow water wave modelling. Part IV: Numerical simulation on a globally spherical geometry, pp.1-40, 2017.
URL : https://hal.archives-ouvertes.fr/hal-01547833

G. S. Khakimzyanov, D. Dutykh, D. E. Mitsotakis, and N. Y. Shokina, Numerical solution of conservation laws on moving grids, pp.1-28

J. W. Kim, K. J. Bai, R. C. Ertekin, and W. C. Webster, A derivation of the Green-Naghdi equations for irrotational flows, Journal of Engineering Mathematics, vol.40, issue.1, pp.17-42, 2001.
DOI : 10.1023/A:1017541206391

J. W. Kim and R. C. Ertekin, A numerical study of nonlinear wave interaction in regular and irregular seas: irrotational Green???Naghdi model, Marine Structures, vol.13, issue.4-5, pp.331-347, 2000.
DOI : 10.1016/S0951-8339(00)00015-0

H. O. Kreiss and G. Scherer, Method of Lines for Hyperbolic Differential Equations, SIAM Journal on Numerical Analysis, vol.29, issue.3, pp.640-646, 1992.
DOI : 10.1137/0729041

A. A. Kurkin, S. V. Semin, and Y. A. Stepanyants, Transformation of surface waves over a bottom step. Izvestiya, Atmospheric and Oceanic Physics, pp.214-223, 2015.

Z. Lai, C. Chen, G. W. Cowles, and R. C. Beardsley, A nonhydrostatic version of FVCOM: 1. Validation experiments, Journal of Geophysical Research, vol.48, issue.2, pp.11010-11051, 2010.
DOI : 10.1017/CBO9780511608827

O. , L. Métayer, S. Gavrilyuk, and S. Hank, A numerical scheme for the Green-Naghdi model, J. Comp. Phys, vol.229, issue.6 6, pp.2034-2045, 2010.

D. Y. Le-roux, Spurious inertial oscillations in shallow-water models, Journal of Computational Physics, vol.231, issue.24, pp.7959-7987, 2012.
DOI : 10.1016/j.jcp.2012.04.052

URL : https://hal.archives-ouvertes.fr/hal-00864893

E. K. Lindstrøm, G. K. Pedersen, A. Jensen, and S. Glimsdal, Experiments on slide generated waves in a 1:500 scale fjord model, Coastal Engineering, vol.92, pp.12-23
DOI : 10.1016/j.coastaleng.2014.06.010

P. L. Liu, T. Wu, F. Raichlen, C. E. Synolakis, and J. C. Borrero, Runup and rundown generated by three-dimensional sliding masses, Journal of Fluid Mechanics, vol.536, issue.1, pp.107-144, 2005.
DOI : 10.1017/S0022112005004799

F. Løvholt, G. Pedersen, and G. Gisler, Oceanic propagation of a potential tsunami from the La Palma Island, Journal of Geophysical Research, vol.294, issue.17, pp.9026-9075, 2008.
DOI : 10.1007/978-94-010-0093-2_36

P. Lynett and P. L. Liu, A numerical study of submarine-landslide-generated waves and run-up, Proc. R. Soc. A, pp.4582885-2910, 2002.
DOI : 10.1098/rspa.2002.0973

O. S. Madsen and C. C. Mei, The transformation of a solitary wave over an uneven bottom, Journal of Fluid Mechanics, vol.20, issue.04, pp.781-791, 1969.
DOI : 10.1029/JZ071i002p00393

P. A. Madsen, H. B. Bingham, and H. Liu, A new Boussinesq method for fully nonlinear waves from shallow to deep water, Journal of Fluid Mechanics, vol.462, pp.1-30, 2002.
DOI : 10.1017/S0022112002008467

P. A. Madsen, R. Murray, and O. R. Sorensen, A new form of the Boussinesq equations with improved linear dispersion characteristics, Coastal Engineering, vol.15, issue.4, pp.371-388, 1991.
DOI : 10.1016/0378-3839(91)90017-B

P. A. Madsen and O. R. Sorensen, A new form of the Boussinesq equations with improved linear dispersion characteristics. Part 2. A slowly-varying bathymetry, Coastal Engineering, vol.18, issue.3-4, pp.183-204, 1992.
DOI : 10.1016/0378-3839(92)90019-Q

S. V. Manoylin, Some experimental and theoretical methods of estimation of tsunami wave action on hydro-technical structures and seaports, p.39, 1989.

T. Maxworthy, Experiments on collisions between solitary waves, Journal of Fluid Mechanics, vol.33, issue.01, pp.177-185, 1976.
DOI : 10.1063/1.1666400

J. W. Miles and R. Salmon, Weakly dispersive nonlinear gravity waves, Journal of Fluid Mechanics, vol.9, issue.-1, pp.519-531, 1985.
DOI : 10.1016/0378-4371(81)90149-7

S. M. Mirie and C. H. Su, Collisions between two solitary waves. Part 2. A numerical study, Journal of Fluid Mechanics, vol.95, issue.-1, pp.475-492, 1982.
DOI : 10.1017/S0022112071002295

D. Mitsotakis, B. Ilan, and D. Dutykh, On the Galerkin/Finite-Element Method for the Serre Equations, Journal of Scientific Computing, vol.73, issue.6, pp.166-195, 2014.
DOI : 10.1016/j.coastaleng.2012.09.005

URL : https://hal.archives-ouvertes.fr/hal-00834064

E. Pelinovsky, B. H. Choi, T. Talipova, S. B. Wood, and D. C. Kim, Solitary wave transformation on the underwater step: Asymptotic theory and numerical experiments, Applied Mathematics and Computation, vol.217, issue.4, pp.1704-1718
DOI : 10.1016/j.amc.2009.10.029

D. H. Peregrine, Calculations of the development of an undular bore, Journal of Fluid Mechanics, vol.224, issue.02, pp.321-330
DOI : 10.1007/BF00384031

D. H. Peregrine, Long waves on a beach, Journal of Fluid Mechanics, vol.13, issue.04, pp.815-827, 1967.
DOI : 10.1029/JZ071i002p00393

B. Ranguelov, S. Tinti, G. Pagnoni, R. Tonini, F. Zaniboni et al., The nonseismic tsunami observed in the Bulgarian Black Sea on 7 May 2007: Was it due to a submarine landslide?, Geophysical Research Letters, vol.28, issue.18, pp.18613-18661, 2007.
DOI : 10.1007/978-94-010-0205-9_24

S. C. Reddy and L. N. Trefethen, Stability of the method of lines, Numerische Mathematik, vol.33, issue.1, pp.235-267, 1992.
DOI : 10.1007/BF01396228

G. Sadaka, Solution of 2D Boussinesq systems with freefem++: the flat bottom case, Journal of Numerical Mathematics, vol.20, issue.3-4, pp.303-324, 2005.
DOI : 10.1515/jnum-2012-0016

URL : https://hal.archives-ouvertes.fr/hal-00697129

A. A. Samarskii, The Theory of Difference Schemes, p.26, 2001.

W. E. Schiesser, Method of lines solution of the Korteweg-de vries equation, Computers Mathematics with Applications, vol.28, issue.6, pp.10-12147, 1994.

F. J. Seabra-santos, D. P. Renouard, and A. M. Temperville, Numerical and experimental study of the transformation of a solitary wave over a shelf or isolated obstacle, Journal of Fluid Mechanics, vol.274, issue.-1, pp.117-134, 1987.
DOI : 10.1080/14786449408620643

F. J. Seabra-santos, A. M. Temperville, and D. P. Renouard, On the weak interaction of two solitary waves, Eur. J. Mech. B/Fluids, vol.8, issue.2, pp.103-115, 1989.

F. Serre, Contribution à l'étude des écoulements permanents et variables dans les canaux, pp.830-872, 1953.

F. Serre, Contribution to the study of long irrotational waves, pp.374-388, 1956.

L. F. Shampine, ODE solvers and the method of lines, Numerical Methods for Partial Differential Equations, vol.33, issue.6, pp.739-755, 1994.
DOI : 10.1016/B978-0-12-436640-4.50017-4

Y. I. Shokin, Y. V. Sergeeva, and G. S. Khakimzyanov, Predictor???corrector scheme for the solution of shallow water equations, Russian Journal of Numerical Analysis and Mathematical Modelling, vol.21, issue.5, pp.459-479, 2006.
DOI : 10.1061/(ASCE)0733-9429(2003)129:1(11)

G. Söderlind and L. Wang, Adaptive time-stepping and computational stability, Journal of Computational and Applied Mathematics, vol.185, issue.2, pp.225-243, 2006.
DOI : 10.1016/j.cam.2005.03.008

O. R. Sørensen, H. A. Schäffer, and L. S. Sørensen, Boussinesq-type modelling using an unstructured finite element technique, Coastal Engineering, vol.50, issue.4, pp.181-198, 2004.
DOI : 10.1016/j.coastaleng.2003.10.005

C. H. Su and R. M. Mirie, On head-on collisions between two solitary waves, Journal of Fluid Mechanics, vol.46, issue.03, pp.509-525, 1980.
DOI : 10.1103/PhysRevLett.19.1095

D. R. Tappin, P. Watts, and S. T. Grilli, The Papua New Guinea tsunami of 17 July 1998: anatomy of a catastrophic event, Natural Hazards and Earth System Science, vol.8, issue.2, pp.243-266, 1998.
DOI : 10.5194/nhess-8-243-2008

URL : https://hal.archives-ouvertes.fr/hal-00299504

P. D. Thomas and C. K. Lombart, Geometric Conservation Law and Its Application to Flow Computations on Moving Grids, AIAA Journal, vol.2, issue.10, pp.1030-1037, 1979.
DOI : 10.2514/3.60840

A. N. Tikhonov and A. A. Samarskii, Homogeneous difference schemes, USSR Computational Mathematics and Mathematical Physics, vol.1, issue.1, pp.5-63, 1961.
DOI : 10.1016/0041-5553(62)90005-8

A. N. Tikhonov and A. A. Samarskii, Homogeneous difference schemes on non-uniform nets, USSR Computational Mathematics and Mathematical Physics, vol.2, issue.5, pp.812-832, 1962.
DOI : 10.1016/0041-5553(63)90505-6

S. Tinti, E. Bortolucci, and C. Vannini, A Block-Based Theoretical Model Suited to Gravitational Sliding, Natural Hazards, vol.16, issue.1, pp.1-28, 1997.
DOI : 10.1023/A:1007934804464

J. Touboul and E. Pelinovsky, Bottom pressure distribution under a solitonic wave reflecting on a vertical wall, European Journal of Mechanics - B/Fluids, vol.48, pp.13-18, 2014.
DOI : 10.1016/j.euromechflu.2014.03.011

URL : https://hal.archives-ouvertes.fr/hal-01203301

M. Walkley and M. Berzins, A finite element method for the two-dimensional extended Boussinesq equations, International Journal for Numerical Methods in Fluids, vol.7, issue.10, pp.865-885, 2002.
DOI : 10.1002/fld.349

S. N. Ward, Landslide tsunami, Journal of Geophysical Research: Solid Earth, vol.145, issue.30, pp.11201-11215, 2001.
DOI : 10.1006/icar.1999.6336

P. Watts, S. T. Grilli, J. T. Kirby, G. J. Fryer, and D. R. Tappin, Landslide tsunami case studies using a Boussinesq model and a fully nonlinear tsunami generation model, Natural Hazards and Earth System Science, vol.3, issue.5, pp.391-402, 2003.
DOI : 10.5194/nhess-3-391-2003

URL : https://hal.archives-ouvertes.fr/hal-00299049

P. Watts, F. Imamura, and S. T. Grilli, Comparing model simulations of three benchmark tsunami generation cases, Science of Tsunami Hazards, vol.18, issue.2, pp.107-123, 2000.

G. Wei and J. T. Kirby, Time-Dependent Numerical Code for Extended Boussinesq Equations, Journal of Waterway, Port, Coastal, and Ocean Engineering, vol.121, issue.5, pp.251-261, 1995.
DOI : 10.1061/(ASCE)0733-950X(1995)121:5(251)

N. N. Zagryadskaya, S. V. Ivanova, L. S. Nudner, and A. I. Shoshin, Action of long waves on a vertical obstacle, Bulletin of VNIIG, vol.138, issue.38, pp.94-101, 1980.

V. E. Zakharov, What Is Integrability? Springer Series in Nonlinear Dynamics, p.15, 1991.

Y. Zhang, A. B. Kennedy, N. Panda, C. Dawson, and J. J. Westerink, Boussinesq???Green???Naghdi rotational water wave theory, Coastal Engineering, vol.73, pp.13-27
DOI : 10.1016/j.coastaleng.2012.09.005

B. B. Zhao, R. C. Ertekin, and W. Y. Duan, A comparative study of diffraction of shallow-water waves by high-level IGN and GN equations, Journal of Computational Physics, vol.283, issue.6, pp.129-147, 2015.
DOI : 10.1016/j.jcp.2014.11.020

M. I. Zheleznyak, Influence of long waves on vertical obstacles, Tsunami Climbing a Beach, pp.122-139, 1985.

M. I. Zheleznyak and E. N. Pelinovsky, Physical and mathematical models of the tsunami climbing a beach, Tsunami Climbing a Beach, pp.8-34, 1985.

G. Khakimzyanov, Campus Scientifique , F-73376 Le Bourget-du-Lac Cedex, France E-mail address: Denys.Dutykh@univ-savoie.fr URL: http://www.denys-dutykh.com/ O. Gusev: Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences, Novosibirsk 630090, Russia E-mail address: gusev_oleg_igor@mail, ru N. Yu. Shokina: Institute of Computational Technologies, Siberian Branch of the Russian Academy of Sciences