J. R. Apel, L. A. Ostrovsky, Y. A. Stepanyants, and J. F. Lynch, Internal solitons in the ocean and their effect on underwater sound, The Journal of the Acoustical Society of America, vol.121, issue.2, p.695, 2007.
DOI : 10.1121/1.2395914

R. Barros and S. Gavrilyuk, Dispersive Nonlinear Waves in Two-Layer Flows with Free Surface Part II. Large Amplitude Solitary Waves Embedded into the Continuous Spectrum, Studies in Applied Mathematics, vol.8, issue.3, pp.213-251, 2007.
DOI : 10.1002/cpa.3160130110

R. Barros, S. L. Gavrilyuk, and V. M. Teshukov, Dispersive Nonlinear Waves in Two-Layer Flows with Free Surface. I. Model Derivation and General Properties, Studies in Applied Mathematics, vol.37, issue.3, pp.191-211, 2007.
DOI : 10.1016/0898-1221(95)00035-W

E. Barthélémy, Etude des ondes longues internes et de leur dynamique dans les zones côtières, p.5, 1989.

T. J. Bridges, Multi-symplectic structures and wave propagation, Mathematical Proceedings of the Cambridge Philosophical Society, vol.121, issue.1, pp.147-190, 1997.
DOI : 10.1017/S0305004196001429

T. J. Bridges and N. M. Donaldson, Reappraisal of criticality for two-layer flows and its role in the generation of internal solitary waves, Physics of Fluids, vol.19, issue.7, p.72111, 2007.
DOI : 10.1063/1.2750541

T. J. Bridges and S. Reich, Multi-symplectic integrators: numerical schemes for Hamiltonian PDEs that conserve symplecticity, Physics Letters A, vol.284, issue.4-5, pp.184-193, 2001.
DOI : 10.1016/S0375-9601(01)00294-8

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, 2016.
DOI : 10.1088/1751-8113/49/3/03LT01

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

W. Choi and R. Camassa, Fully nonlinear internal waves in a two-fluid system, Journal of Fluid Mechanics, vol.396, issue.4, pp.1-36, 1999.
DOI : 10.1017/S0022112099005820

P. Christodoulides and F. Dias, Stability of capillary???gravity interfacial waves between two bounded fluids, Physics of Fluids, vol.7, issue.12, p.3013, 1995.
DOI : 10.1063/1.868678

V. Duchêne, S. Israwi, and R. Talhouk, A New Class of Two-Layer Green-Naghdi Systems with Improved Frequency Dispersion, Studies in Applied Mathematics, vol.184, issue.6, 2016.
DOI : 10.1111/sapm.12125

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

C. Garrett and W. Munk, Space-time scales of internal waves: A progress report, Journal of Geophysical Research, vol.19, issue.52, pp.291-297, 1975.
DOI : 10.1029/JC080i003p00291

C. Garrett and W. Munk, Internal Waves in the Ocean, Annual Review of Fluid Mechanics, vol.11, issue.1, pp.339-369, 1979.
DOI : 10.1146/annurev.fl.11.010179.002011

R. S. Johnson, Camassa???Holm, Korteweg???de Vries and related models for water waves, Journal of Fluid Mechanics, vol.455, issue.4, pp.63-82, 2002.
DOI : 10.1017/S0022112001007224

Z. L. Maltseva, Unsteady long waves in a two-layer fluid. Dinamika Sploshn. Sredy, pp.93-9496, 1989.

J. E. Marsden, G. W. Patrick, and S. Shkoller, Multisymplectic Geometry, Variational Integrators, and Nonlinear PDEs, Communications in Mathematical Physics, vol.199, issue.2, p.52, 1998.
DOI : 10.1007/s002200050505

M. Miyata, Long Internal Waves of Large Amplitude, Nonlinear Water Waves: IUTAM Symposium, pp.399-405, 1987.
DOI : 10.1007/978-3-642-83331-1_44

B. Moore and S. Reich, Multi-symplectic integration methods for Hamiltonian PDEs, Future Generation Computer Systems, vol.19, issue.3, pp.395-402, 2003.
DOI : 10.1016/S0167-739X(02)00166-8

L. Ostrovsky, E. Pelinovsky, V. Shrira, and Y. Stepanyants, Beyond the KdV: Post-explosion development, Chaos: An Interdisciplinary Journal of Nonlinear Science, vol.25, issue.9, pp.97620-2015
DOI : 10.1063/1.4927448

F. Serre, Contribution à l'étude des écoulements permanents et variables dans les canaux, pp.374-388, 1953.

R. Staub, Contribution à l'étude des ondes de gravité en eau peu profonde, 1972.