M. J. Ablowitz, D. Klaup, A. Newell, and H. Segur, The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems, Studies in Applied Mathematics, vol.34, issue.12, pp.249-315, 1974.
DOI : 10.1103/PhysRevLett.15.240

M. J. Ablowitz, M. D. Kruskal, and J. F. Ladik, Solitary Wave Collisions, SIAM Journal on Applied Mathematics, vol.36, issue.3, pp.428-437, 1979.
DOI : 10.1137/0136033

M. Alejo and C. Muñoz, Nonlinear Stability of MKdV Breathers, Communications in Mathematical Physics, vol.39, issue.3, pp.233-262, 2013.
DOI : 10.1002/cpa.3160390103
URL : http://arxiv.org/pdf/1206.3157.pdf

M. Beceanu, A Centre-Stable Manifold for the Focussing Cubic NLS in $${\mathbb{R}}^{1+3}$$, Communications in Mathematical Physics, vol.259, issue.2, pp.145-205, 2008.
DOI : 10.1353/ajm.2007.0021
URL : http://arxiv.org/pdf/math/0701785

M. Beceanu, A critical center-stable manifold for Schr??dinger's equation in three dimensions, Communications on Pure and Applied Mathematics, vol.39, issue.4, pp.431-507, 2012.
DOI : 10.1002/cpa.3160390103

T. B. Benjamin, The Stability of Solitary Waves, Proc. Roy. Soc. London A 328, pp.153-183, 1972.
DOI : 10.1098/rspa.1972.0074

H. Berestycki and P. Lions, Nonlinear scalar field equations, I existence of a ground state, Archive for Rational Mechanics and Analysis, vol.82, issue.4, pp.313-345, 1983.
DOI : 10.1007/BF00250555

J. L. Bona, On the Stability Theory of Solitary Waves, Proc. Roy. Soc. London A 349, pp.363-374, 1975.
DOI : 10.1098/rspa.1975.0106

J. L. Bona, W. G. Pritchard, and L. R. Scott, Solitary-wave interaction, Physics of Fluids, vol.56, issue.3, p.438, 1980.
DOI : 10.1016/0375-9601(76)90714-3

J. L. Bona, P. E. Souganidis, and W. A. Strauss, Stability and Instability of Solitary Waves of Korteweg-de Vries Type, Proc. Roy. Soc. London Ser. A 411, pp.395-412, 1987.
DOI : 10.1098/rspa.1987.0073

M. Borghese, R. Jenkins, and K. T. Mclaughlin, Long-time asymptotic behavior of the focusing nonlinear Schrödinger equation, pp.1604-07436
DOI : 10.1016/j.anihpc.2017.08.006
URL : http://arxiv.org/pdf/1604.07436

V. Buslaev and G. Perelman, Scattering for the nonlinear Schrödinger equations: states close to a soliton, St. Petersburgh Math. J, vol.4, issue.6, pp.1111-1142, 1993.

V. Buslaev and G. Perelman, On the stability of solitary waves for nonlinear Schrödinger equations. Nonlinear evolution equations, Amer. Math. Soc. Transl. Ser, vol.2, issue.164, pp.75-98, 1995.

V. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schr??dinger equations, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.20, issue.3, pp.419-475, 2003.
DOI : 10.1016/S0294-1449(02)00018-5
URL : https://doi.org/10.1016/s0294-1449(02)00018-5

T. Cazenave, Semilinear Schrödinger equations, 2003.

T. Cazenave and P. L. Lions, Orbital stability of standing waves for some nonlinear Schr???dinger equations, Communications in Mathematical Physics, vol.49, issue.4, pp.549-561, 1982.
DOI : 10.1002/sapm197757293

A. Cohen, Existence and regularity for solutions of the Korteweg-de Vries equation, Archive for Rational Mechanics and Analysis, vol.15, issue.2, pp.143-175, 1979.
DOI : 10.1002/cpa.3160320202

V. Combet, Multi-Soliton Solutions for the Supercritical gKdV Equations, Communications in Partial Differential Equations, vol.14, issue.3, pp.380-419, 2010.
DOI : 10.1002/cpa.3160390103
URL : https://hal.archives-ouvertes.fr/hal-00456077

V. Combet, Multi-existence of multi-solitons for the supercritical nonlinear Schr??dinger equation in one dimension, Discrete and Continuous Dynamical Systems, vol.34, issue.5, pp.1961-1993, 2014.
DOI : 10.3934/dcds.2014.34.1961

V. Combet and Y. Martel, Sharp asymptotics for the minimal mass blow up solution of the critical gKdV equation, Bulletin des Sciences Math??matiques, vol.141, issue.2, pp.20-103, 2017.
DOI : 10.1016/j.bulsci.2017.01.001
URL : https://hal.archives-ouvertes.fr/hal-01708194

V. Combet and Y. Martel, Construction of multi-bubble solutions for the critical gKdV equation
URL : https://hal.archives-ouvertes.fr/hal-01708243

O. Costin, M. Huang, and W. Schlag, in three dimensions, Nonlinearity, vol.25, issue.1, pp.125-164, 2012.
DOI : 10.1088/0951-7715/25/1/125

R. Côte, On the soliton resolution for equivariant wave maps to the sphere, Comm. Pure Appl. Math, vol.68, issue.11, 1946.

R. Côte, C. E. Kenig, A. Lawrie, and W. Schlag, Characterization of large energy solutions of the equivariant wave map problem: I, American Journal of Mathematics, vol.137, issue.1, pp.139-207, 2015.
DOI : 10.1353/ajm.2015.0002

R. Côte, C. E. Kenig, A. Lawrie, and W. Schlag, Characterization of large energy solutions of the equivariant wave map problem: II, American Journal of Mathematics, vol.137, issue.1, pp.209-250, 2015.
DOI : 10.1353/ajm.2015.0003

R. Côte and Y. Martel, Multi-travelling waves for the nonlinear Klein-Gordon equation. To appear in Trans, Amer. Math. Soc

R. Côte, Y. Martel, and F. Merle, Construction of multi-soliton solutions for the L 2 -supercritical gKdV and NLS equations, Rev. Mat. Iberoamericana, vol.27, pp.273-302, 2011.

R. Côte and C. Muñoz, Multi-solitons for nonlinear Klein-Gordon equations, Forum of Mathematics, issue.2, 2014.

W. Craig, P. Guyenne, J. Hammack, D. Henderson, and C. Sulem, Solitary water wave interactions, Physics of Fluids, vol.8, issue.5, p.57106, 2006.
DOI : 10.1137/S1111111102411298

S. Cuccagna, On asymptotic stability in 3D of kinks for the $\phi ^4$ model, Transactions of the American Mathematical Society, vol.360, issue.05, pp.2581-2614, 2008.
DOI : 10.1090/S0002-9947-07-04356-5

S. Cuccagna, On asymptotic stability of moving ground states of the nonlinear Schr??dinger equation, Transactions of the American Mathematical Society, vol.366, issue.6, pp.2827-2888, 2014.
DOI : 10.1090/S0002-9947-2014-05770-X

S. Cuccagna and D. Pelinovsky, The asymptotic stability of solitons in the cubic NLS equation on the line, Applicable Analysis, vol.44, issue.4, pp.791-822, 2014.
DOI : 10.1017/CBO9780511608759

S. Cuenda, N. R. Quintero, and A. Sánchez, Sine-Gordon wobbles through Bäcklund transformations, Discrete and Continuous Dynamical Systems -Series S, pp.1047-1056, 2011.
DOI : 10.3934/dcdss.2011.4.1047
URL : https://doi.org/10.3934/dcdss.2011.4.1047

T. Dauxois and M. Peyrard, Physics of solitons, 2010.

P. Deift and E. Trubowitz, Inverse scattering on the line, Communications on Pure and Applied Mathematics, vol.45, issue.2, pp.121-251, 1979.
DOI : 10.1007/BF02745417

P. Deift, S. Venakides, and X. Zhou, The collisionless shock region for the long-time behavior of solutions of the KdV equation, Communications on Pure and Applied Mathematics, vol.44, issue.2, pp.199-206, 1994.
DOI : 10.1007/BFb0076661

P. A. Deift and X. Zhou, Long-time asymptotics for integrable nonlinear wave equations. Important developments in soliton theory, pp.181-204, 1993.
DOI : 10.1007/978-3-642-58045-1_10

P. A. Deift and X. Zhou, Perturbation theory for infinite-dimensional integrable systems on the line. A case study, Acta Mathematica, vol.188, issue.2, pp.163-262, 2002.
DOI : 10.1007/BF02392683
URL : http://doi.org/10.1007/bf02392683

R. K. Dodd, J. C. Eilbeck, J. D. Gibbona, and H. C. Morris, Solitons and nonlinear wave equations, 1982.

T. Duyckaerts and F. Merle, Dynamics of Threshold Solutions for Energy-Critical Wave Equation, International Mathematics Research Papers, vol.4, 2008.
DOI : 10.1353/ajm.2007.0021

T. Duyckaerts, C. E. Kenig, and F. Merle, Universality of blow-up profile for small radial type II blow-up solutions of the energy-critical wave equation, Journal of the European Mathematical Society, pp.13-533, 2011.
DOI : 10.4171/JEMS/261
URL : https://hal.archives-ouvertes.fr/hal-00460872

T. Duyckaerts, C. E. Kenig, and F. Merle, Universality of the blow-up profile for small type II blow-up solutions of the energy-critical wave equation: the nonradial case, Journal of the European Mathematical Society, vol.14, issue.5, pp.1389-1454, 2012.
DOI : 10.4171/JEMS/336
URL : https://hal.archives-ouvertes.fr/hal-00460872

T. Duyckaerts, C. E. Kenig, and F. Merle, Classification of the radial solutions of the focusing, energy-critical wave equation, Cambridge Journal of Mathematics, vol.1, issue.1, pp.75-144, 2013.
DOI : 10.4310/CJM.2013.v1.n1.a3

T. Duyckaerts, C. E. Kenig, and F. Merle, Solutions of the focusing nonradial critical wave equation with the compactness property, Ann. Sc. Norm. Super. Pisa Cl. Sci, issue.5, pp.15-731, 2016.

T. Duyckaerts, H. Jia, C. E. Kenig, and F. Merle, Soliton resolution along a sequence of times for the focusing energy critical wave equation, Geometric and Functional Analysis, vol.45, issue.3, pp.798-862, 2017.
DOI : 10.4310/jdg/1214459844

W. Eckhaus and P. Schuur, The emergence of solitons of the korteweg-de vries equation from arbitrary initial conditions, Mathematical Methods in the Applied Sciences, vol.59, issue.1, pp.97-116, 1983.
DOI : 10.1017/S0022112073001813

S. Ei and T. Ohta, The motion of interacting pulses, Phys. Rev, vol.50, pp.4672-4678, 1994.
DOI : 10.1103/physreve.50.4672

L. D. Faddeev and L. A. Takhtajan, Hamiltonian Methods in the Theory of Solitons. Translated from the 1986 Russian original by Alexey G. Reyman. Reprint of the 1987 English edition, Classics in Mathematics, 2007.

E. Fermi, J. Pasta, and S. Ulam, Studies of nonlinear problems, I, Los Alamos Report LA1940 (1955); reproduced in Nonlinear Wave Motion, pp.143-156, 1974.

C. S. Gardner, C. S. Greene, M. D. Kruskal, and R. M. Miura, Method for Solving the Korteweg-deVries Equation, Physical Review Letters, vol.27, issue.19, pp.1095-1087, 1967.
DOI : 10.1063/1.1722296

C. S. Gardner, C. S. Greene, M. D. Kruskal, and R. M. Miura, Korteweg-devries equation and generalizations. VI. methods for exact solution, Communications on Pure and Applied Mathematics, vol.5, issue.1, pp.97-133, 1974.
DOI : 10.1080/14786449508620739

P. Gérard, E. Lenzmann, O. Pocovnicu, and P. , A Two-Soliton with Transient Turbulent Regime for the Cubic Half-Wave Equation on the Real Line, Annals of PDE, vol.152, issue.153, pp.1611-08482
DOI : 10.1016/S0167-2789(01)00194-4

S. Gustafson, K. Nakanishi, and T. Tsai, Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves, Int. Math. Res. Not, issue.66, pp.3559-3584, 2004.

P. Germain, F. Pusateri, and F. Rousset, Asymptotic stability of solitons for mKdV, Advances in Mathematics, vol.299, pp.272-330, 2016.
DOI : 10.1016/j.aim.2016.04.023
URL : https://manuscript.elsevier.com/S0001870816305357/pdf/S0001870816305357.pdf

J. Ginibre and G. Velo, On a class of nonlinear Schr??dinger equations. I. The Cauchy problem, general case, Journal of Functional Analysis, vol.32, issue.1, pp.1-32, 1979.
DOI : 10.1016/0022-1236(79)90076-4

K. A. Gorshkov and L. A. Ostrovsky, Interactions of solitons in nonintegrable systems: Direct perturbation method and applications, Physica D: Nonlinear Phenomena, vol.3, issue.1-2, pp.428-438, 1981.
DOI : 10.1016/0167-2789(81)90146-9

M. Grillakis, Linearized instability for nonlinear schr??dinger and klein-gordon equations, Communications on Pure and Applied Mathematics, vol.16, issue.6, pp.747-774, 1988.
DOI : 10.1090/conm/017/706117

M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry, I, Journal of Functional Analysis, vol.74, issue.1, pp.160-197, 1987.
DOI : 10.1016/0022-1236(87)90044-9

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

N. Hayashi and P. Naumkin, Large Time Asymptotics of Solutions to the Generalized Korteweg???de Vries Equation, Journal of Functional Analysis, vol.159, issue.1, pp.110-136, 1998.
DOI : 10.1006/jfan.1998.3291

N. Hayashi and P. Naumkin, On the modified Korteweg-de Vries equation, International Seminar. Day on Diffraction. Proceedings (IEEE Cat. No.99EX367), pp.197-201, 2001.
DOI : 10.1109/DD.1999.816195

D. B. Henry, J. F. Perez, and W. F. Wreszinski, Stability theory for solitary-wave solutions of scalar field equations, Communications in Mathematical Physics, vol.55, issue.3, pp.351-361, 1982.
DOI : 10.1007/978-1-4612-6374-6

R. Hirota, Exact Solution of the Korteweg???de Vries Equation for Multiple Collisions of Solitons, Physical Review Letters, vol.11, issue.18, pp.1192-1194, 1971.
DOI : 10.1063/1.1665057

J. Holmer and M. Zworski, Slow soliton interaction with delta impurities, J. Mod. Dyn, vol.1, issue.4, pp.689-718, 2007.

J. Holmer and M. Zworski, Soliton Interaction with Slowly Varying Potentials, International Mathematics Research Notices, vol.29, issue.4, 2008.
DOI : 10.1093/imrn/rnn026

J. Holmer, J. Marzuola, and M. Zworski, Soliton Splitting by External Delta Potentials, Journal of Nonlinear Science, vol.17, issue.4, pp.349-367, 2007.
DOI : 10.1007/s00332-006-0807-9

J. Holmer, J. Marzuola, and M. Zworski, Fast Soliton Scattering by Delta Impurities, Communications in Mathematical Physics, vol.34, issue.1, pp.187-216, 2007.
DOI : 10.1007/s00220-004-1128-1

J. Jendrej, Construction of type II blow-up solutions for the energy-critical wave equation in dimension 5, Journal of Functional Analysis, vol.272, issue.3, pp.866-917, 2017.
DOI : 10.1016/j.jfa.2016.10.019

J. Jendrej, Construction of two-bubble solutions for energy-critical wave equations. To appear in Amer, J. Math. Preprint

J. Jendrej and A. Lawrie, Two-bubble dynamics for threshold solutions to the wave maps equation, Inventiones mathematicae, vol.123, issue.1, pp.1706-00089
DOI : 10.1353/ajm.2001.0005

R. Jenkins, J. Liu, P. Perry, and C. Sulem, Soliton resolution for the derivative non-linear Schrödinger equation, pp.1710-03819

V. I. Karpman and V. V. , Solov'ev, A perturbational approach to the two-soliton systems, Physica, vol.3, pp.487-502, 1981.

T. Kato, On the Cauchy problem for the (generalized) Korteweg?de Vries equation Advances in Mathematical Supplementary Studies, Studies in Applied Math, vol.8, pp.93-128, 1983.

C. E. Kenig, A. Lawrie, B. Liu, and W. Schlag, Channels of energy for the linear radial wave equation, Advances in Mathematics, vol.285, pp.877-936, 2015.
DOI : 10.1016/j.aim.2015.08.014

C. E. Kenig, A. Lawrie, and W. Schlag, Relaxation of Wave Maps Exterior to a Ball to Harmonic Maps for All Data, Geometric and Functional Analysis, vol.41, issue.4, pp.610-647, 2014.
DOI : 10.1002/cpa.3160410405

C. E. Kenig and Y. Martel, Asymptotic stability of solitons for the Benjamin-Ono equation, Revista Matem??tica Iberoamericana, vol.25, pp.909-970, 2009.
DOI : 10.4171/RMI/586
URL : https://hal.archives-ouvertes.fr/hal-00408107

C. E. Kenig and F. Merle, Global well-posedness, scattering and blow-up for the energy-critical focusing non-linear wave equation, Acta Mathematica, vol.201, issue.2, pp.147-212, 2008.
DOI : 10.1007/s11511-008-0031-6
URL : https://hal.archives-ouvertes.fr/hal-00174402

C. E. Kenig, G. Ponce, and L. Vega, Well-posedness and scattering results for the generalized korteweg-de vries equation via the contraction principle, Communications on Pure and Applied Mathematics, vol.34, issue.4, pp.46-527, 1993.
DOI : 10.1007/978-1-4612-0431-2

Y. S. Kivshar and B. Malomed, Dynamics of solitons in nearly integrable models, Review of Modern Physics, pp.61-763, 1989.
DOI : 10.1103/revmodphys.61.763

E. Kopylova and A. I. Komech, On Asymptotic Stability of Kink for Relativistic Ginzburg???Landau Equations, Archive for Rational Mechanics and Analysis, vol.16, issue.3, pp.213-245, 2011.
DOI : 10.1137/0516034

E. Kopylova and A. I. Komech, On Asymptotic Stability of Moving Kink for Relativistic Ginzburg-Landau Equation, Communications in Mathematical Physics, vol.55, issue.2, pp.225-252, 2011.
DOI : 10.1002/cpa.3012
URL : http://arxiv.org/pdf/0910.5538

M. Kowalczyk, Y. Martel, and C. Muñoz, Kink dynamics in the $\phi ^4$ model: Asymptotic stability for odd perturbations in the energy space, Journal of the American Mathematical Society, vol.30, issue.3, pp.769-798, 2017.
DOI : 10.1090/jams/870
URL : https://hal.archives-ouvertes.fr/hal-01708213

M. Kowalczyk, Y. Martel, and C. Muñoz, On asymptotic stability of nonlinear waves, S??minaire Laurent Schwartz ??? EDP et applications, vol.27, issue.18, 2016.
DOI : 10.5802/slsedp.111
URL : http://slsedp.cedram.org/cedram-bin/article/SLSEDP_2016-2017____A18_0.pdf

J. Krieger, Y. Martel, and P. , Two-soliton solutions to the three-dimensional gravitational Hartree equation, Communications on Pure and Applied Mathematics, vol.61, issue.1, pp.1501-1550, 2009.
DOI : 10.1353/ajm.2005.0033
URL : https://hal.archives-ouvertes.fr/hal-00408105

J. Krieger, K. Nakanishi, and W. Schlag, Threshold Phenomenon for the Quintic Wave Equation in Three Dimensions, Communications in Mathematical Physics, vol.1, issue.2, pp.309-332, 2014.
DOI : 10.1007/BF02761595
URL : http://www.math.upenn.edu/~kriegerj/papers/Threshold2.pdf

J. Krieger, K. Nakanishi, and W. Schlag, Global dynamics away from the ground state for the energy-critical nonlinear wave equation, American Journal of Mathematics, vol.135, issue.4, pp.935-965, 2013.
DOI : 10.1353/ajm.2013.0034
URL : http://arxiv.org/pdf/1010.3799

J. Krieger, W. Schlag, and D. Tataru, Slow blow-up solutions for the H 1 (R 3 ) critical focusing semilinear wave equation. Duke Math, J, vol.147, issue.1, pp.1-53, 2009.
DOI : 10.1215/00127094-2009-005
URL : https://infoscience.epfl.ch/record/155188/files/slow0201.pdf

M. D. , The Korteweg-de Vries equation and related evolution equations, in Nonlinear Wave Motion, pp.61-83, 1974.

S. B. Kuksin, Analysis of Hamiltonian PDEs, Oxford Lecture Series in Mathematics and its Applications, vol.19, 2000.

M. K. Kwong, Uniqueness of positive solutions of ??u???u+up=0 in Rn, Archive for Rational Mechanics and Analysis, vol.61, issue.3, pp.243-266, 1989.
DOI : 10.1016/0022-0396(86)90112-9

G. L. Lamb-jr, Element of soliton theory, 1980.

P. D. Lax, Integrals of nonlinear equations of evolution and solitary waves, Communications on Pure and Applied Mathematics, vol.15, issue.5, pp.467-490, 1968.
DOI : 10.1080/14786449508620739

R. Leveque, On the Interaction of Nearly Equal Solitons in the KdV Equation, SIAM Journal on Applied Mathematics, vol.47, issue.2, pp.254-262, 1987.
DOI : 10.1137/0147017

Y. Li and D. H. Sattinger, Soliton Collisions in the Ion Acoustic Plasma Equations, Journal of Mathematical Fluid Mechanics, vol.1, issue.1, pp.117-130, 1999.
DOI : 10.1007/s000210050006

N. Manton and P. Sutcliffe, Topological solitons, Cambridge Monographs on Mathematical Physics, 2004.

Y. Martel, Asymptotic N -soliton-like solutions of the subcritical and critical generalized Korteweg-de Vries equations, American Journal of Mathematics, vol.127, issue.5, pp.1103-1140, 2005.
DOI : 10.1353/ajm.2005.0033

Y. Martel and F. Merle, A Liouville theorem for the critical generalized Korteweg???de Vries equation, Journal de Math??matiques Pures et Appliqu??es, vol.79, issue.4, pp.339-425, 2000.
DOI : 10.1016/S0021-7824(00)00159-8
URL : https://hal.archives-ouvertes.fr/hal-00189839

Y. Martel and F. Merle, Asymptotic Stability of Solitons??for Subcritical Generalized KdV Equations, Archive for Rational Mechanics and Analysis, vol.157, issue.3, pp.219-254, 2001.
DOI : 10.1007/s002050100138

Y. Martel and F. Merle, Stability of Blow-Up Profile and Lower Bounds for Blow-Up Rate for the Critical Generalized KdV Equation, The Annals of Mathematics, vol.155, issue.1, pp.235-280, 2002.
DOI : 10.2307/3062156
URL : https://hal.archives-ouvertes.fr/hal-00194565

Y. Martel and F. Merle, Asymptotic stability of solitons of the subcritical gKdV equations revisited, Nonlinearity, vol.18, issue.1, pp.55-80, 2005.
DOI : 10.1088/0951-7715/18/1/004
URL : https://hal.archives-ouvertes.fr/hal-00096485

Y. Martel and F. Merle, Multi-solitary waves for nonlinear Schrödinger equations. Annales de l'IHP (C) Non Linear Analysis, pp.849-864, 2006.

Y. Martel and F. Merle, Description of two soliton collision for the quartic gKdV equation, Annals of Mathematics, vol.174, issue.2, pp.757-857, 2011.
DOI : 10.4007/annals.2011.174.2.2
URL : https://hal.archives-ouvertes.fr/hal-00690291

Y. Martel and F. Merle, Inelastic interaction of nearly equal solitons for??the??quartic gKdV equation, Inventiones mathematicae, vol.15, issue.1841, pp.563-648, 2011.
DOI : 10.1103/PhysRevLett.15.240
URL : https://hal.archives-ouvertes.fr/hal-00672816

Y. Martel and F. Merle, On the Nonexistence of Pure Multi-solitons for the Quartic gKdV Equation, International Mathematics Research Notices, vol.15, issue.6, pp.688-739, 2015.
DOI : 10.1103/PhysRevLett.15.240
URL : https://hal.archives-ouvertes.fr/hal-00865178

Y. Martel and F. Merle, Construction of Multi-Solitons for the Energy-Critical Wave Equation in Dimension 5, Archive for Rational Mechanics and Analysis, vol.34, issue.11, pp.1113-1160, 2016.
DOI : 10.1103/PhysRevLett.15.240
URL : https://hal.archives-ouvertes.fr/hal-01708200

Y. Martel and F. Merle, Inelasticity of soliton collisions for the 5D energy critical wave equation, pp.1708-09712
URL : https://hal.archives-ouvertes.fr/hal-01708248

Y. Martel, F. Merle, and P. , Blow up for the critical generalized Korteweg???de Vries equation. I: Dynamics near the soliton, Acta Mathematica, vol.212, issue.1, pp.59-140, 2014.
DOI : 10.1007/s11511-014-0109-2

Y. Martel, F. Merle, and T. Tsai, Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations, Commun. Math. Phys, pp.231-347, 2002.

Y. Martel and P. , Strongly interacting blow up bubbles for the mass critical NLS, Ann. Sci. ´ Ec. Norm. Supér, p.900
URL : https://hal.archives-ouvertes.fr/hal-01808634

F. Merle, Construction of solutions with exactly k blow-up points for the Schr??dinger equation with critical nonlinearity, Communications in Mathematical Physics, vol.14, issue.2, pp.223-240, 1990.
DOI : 10.1007/BF02096981

F. Merle and P. , On universality of blow-up profile for L 2 critical nonlinear Schr???dinger equation, Inventiones Mathematicae, vol.156, issue.3, pp.565-672, 2004.
DOI : 10.1007/s00222-003-0346-z

F. Merle and P. , Profiles and Quantization of the Blow Up Mass for Critical Nonlinear Schr???dinger Equation, Communications in Mathematical Physics, vol.87, issue.3, pp.675-704, 2005.
DOI : 10.1007/s00220-004-1198-0

M. Ming, F. Rousset, and N. Tzvetkov, Multi-solitons and Related Solutions for the Water-waves System, SIAM Journal on Mathematical Analysis, vol.47, issue.1, pp.897-954, 2015.
DOI : 10.1137/140960220
URL : https://hal.archives-ouvertes.fr/hal-00833221

R. M. Miura, The Korteweg???deVries Equation: A Survey of Results, SIAM Review, vol.18, issue.3, pp.412-459, 1976.
DOI : 10.1137/1018076

R. M. Miura, C. S. Gardner, and M. D. , Korteweg???de Vries Equation and Generalizations. II. Existence of Conservation Laws and Constants of Motion, Journal of Mathematical Physics, vol.9, issue.8, pp.1204-1209, 1968.
DOI : 10.1103/PhysRevLett.19.1095

T. Mizumachi, Weak Interaction between Solitary Waves of the Generalized KdV Equations, SIAM Journal on Mathematical Analysis, vol.35, issue.4, pp.1042-1080, 2003.
DOI : 10.1137/S003614100240871X

C. Muñoz, On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity, International Mathematics Research Notices, vol.15, issue.9, pp.1624-1719, 2010.
DOI : 10.1353/ajm.2005.0033

C. Muñoz, Inelastic character of solitons of slowly varying gKdV equations, Comm. Math. Phys, vol.314, issue.3, p.817852, 2012.

C. Muñoz, Dynamics of Soliton-like Solutions for Slowly Varying, Generalized KdV Equations: Refraction versus Reflection, SIAM Journal on Mathematical Analysis, vol.44, issue.1, pp.1-60, 2012.
DOI : 10.1137/100809763

K. Nakanishi and W. Schlag, Invariant manifolds and dispersive Hamiltonian evolution equations, Zurich Lectures in Advanced Mathematics. European Mathematical Society (EMS), 2011.
DOI : 10.4171/095

V. J. Novoksenov, Asymptotic behavior as t ? ? of the solution to the Cauchy problem for a nonlinear Schrödinger equation, Dokl. Akad. Nauk SSSR, vol.251, pp.799-802, 1980.

T. V. Nguyen, Existence of multi-solitary waves with logarithmic relative disctances for the NLS equation, pp.1611-08869

T. V. Nguyen, Strongly interacting multi-solitons with logarithmic relative distance for gKdV equation

E. Olmedilla, Multiple pole solutions of the non-linear Schr??dinger equation, Physica D: Nonlinear Phenomena, vol.25, issue.1-3, pp.330-346, 1987.
DOI : 10.1016/0167-2789(87)90107-2

R. L. Pego and M. I. Weinstein, Eigenvalues, and Instabilities of Solitary Waves, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.340, issue.1656, pp.47-94, 1992.
DOI : 10.1098/rsta.1992.0055

R. L. Pego and M. I. Weinstein, Asymptotic stability of solitary waves, Comm. Math. Phys, pp.164-305, 1994.

G. Perelman, Two soliton collision for nonlinear Schr??dinger equations in dimension 1, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.28, issue.3, pp.357-384, 2011.
DOI : 10.1016/j.anihpc.2011.02.002

P. , On singularity formation in Hamiltonian evolution equations, Proceedings of the International Congress of Mathematicians, p.2014

I. Rodnianski, W. Schlag, and A. Soffer, Dispersive analysis of charge transfer models, Communications on Pure and Applied Mathematics, vol.150, issue.2, pp.149-216, 2005.
DOI : 10.1002/cpa.20066

I. Rodnianski, W. Schlag, and A. Soffer, Asymptotic stability of N -soliton states of NLS, p.309114

W. Schlag, Spectral theory and nonlinear partial differential equations: A survey, Discrete and Continuous Dynamical Systems, vol.15, issue.3, pp.703-723, 2006.
DOI : 10.3934/dcds.2006.15.703

W. Schlag, Dispersive estimates for Schrödinger operators: A survey Mathematical aspects of nonlinear dispersive equations, Ann. of Math. Stud, vol.163, pp.255-285, 2007.

W. Schlag, Stable manifolds for an orbitally unstable nonlinear Schr??dinger equation, Annals of Mathematics, vol.169, issue.1, pp.139-227, 2009.
DOI : 10.4007/annals.2009.169.139

P. C. Schuur, Asymptotic analysis of solitons problems, Lecture Notes in Math, vol.1232, 1986.
DOI : 10.1007/BFb0073054

H. Segur, and sine???Gordon theory, Journal of Mathematical Physics, vol.8, issue.6, pp.1439-1443, 1983.
DOI : 10.1063/1.522391

L. Y. Shih, Soliton-like interaction governed by the generalized Korteweg-de Vries equation, Wave Motion, vol.2, issue.3, pp.197-206, 1980.
DOI : 10.1016/0165-2125(80)90001-3

A. Soffer and W. I. Weinstein, Multichannel nonlinear scattering for nonintegrable equations, Communications in Mathematical Physics, vol.34, issue.1, pp.116-146, 1990.
DOI : 10.1002/sapm1981643225

A. Soffer and M. I. Weinstein, Multichannel nonlinear scattering for nonintegrable equations II. The case of anisotropic potentials and data, Journal of Differential Equations, vol.98, issue.2, pp.376-390, 1992.
DOI : 10.1016/0022-0396(92)90098-8

T. Tao, Nonlinear dispersive equations. Local and global analysis, CBMS Regional Conference Series in Mathematics, vol.106, 2006.

T. Tao, Scattering for the quartic generalised Korteweg???de Vries equation, Journal of Differential Equations, vol.232, issue.2, pp.623-651, 2007.
DOI : 10.1016/j.jde.2006.07.019

T. Tao, Why are solitons stable? Bull. Amer, Math. Soc. (N.S.), vol.46, issue.1, pp.1-33, 2009.

M. Wadati, The Modified Korteweg-de Vries Equation, Journal of the Physical Society of Japan, vol.34, issue.5, pp.1289-1296, 1973.
DOI : 10.1143/JPSJ.34.1289

M. Wadati and K. Ohkuma, Multiple-Pole Solutions of the Modified Korteweg-de Vries Equation, Journal of the Physical Society of Japan, vol.51, issue.6, pp.2029-2035, 1982.
DOI : 10.1143/JPSJ.51.2029

M. Wadati and M. Toda, The Exact N-Soliton Solution of the Korteweg-de Vries Equation, J. Phys. Soc. Japan, vol.32, pp.1403-1411, 1972.
DOI : 10.1142/9789814354332_0021

M. I. Weinstein, Modulational Stability of Ground States of Nonlinear Schr??dinger Equations, SIAM Journal on Mathematical Analysis, vol.16, issue.3, pp.472-491, 1985.
DOI : 10.1137/0516034

M. I. Weinstein, Lyapunov stability of ground states of nonlinear dispersive evolution equations, Communications on Pure and Applied Mathematics, vol.38, issue.1, pp.51-68, 1986.
DOI : 10.1016/0375-9601(83)90534-0

G. B. Whitham, Linear and Nonlinear Waves, 1974.

J. Yang, Nonlinear waves in integrable and nonintegrable systems, Mathematical Modeling and Computation Society for Industrial and Applied Mathematics (SIAM), vol.16, 2010.
DOI : 10.1137/1.9780898719680

N. J. Zabusky and M. D. , Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States, Physical Review Letters, vol.15, issue.6, pp.240-243, 1965.
DOI : 10.1103/PhysRevLett.15.240

N. J. Zakharov and M. D. Manakov, Asymptotic behavior of nonlinear wave systems integrated by the inverse scattering transform, Soviet Physics JETP, vol.44, pp.106-112, 1976.

V. E. Zakharov and A. B. Shabat, Exact theory of two-dimensional self-focusing and one-dimensional self-modulation of waves in nonlinear media, Soviet Physics JETP, vol.34, pp.62-69, 1972.

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