M. J. Ablowitz and P. A. Clarkson, Solitons, nonlinear evolution equations and inverse scattering, 1991.
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W. K. Salem, J. Fröhlich, and I. M. Sigal, Colliding solitons for the nonlinear Schrödinger equation

T. B. Benjamin, The Stability of Solitary Waves, Proc. Roy. Soc. London A 328, pp.153-183, 1972.
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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.
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J. L. Bona, P. Souganidis, and W. Strauss, Stability and Instability of Solitary Waves of Korteweg-de Vries Type, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.411, issue.1841, pp.395-412, 1987.
DOI : 10.1098/rspa.1987.0073

J. C. Bronski and R. L. Jerrard, Soliton dynamics in a potential, Mathematical Research Letters, vol.7, issue.3, pp.329-342, 2000.
DOI : 10.4310/MRL.2000.v7.n3.a7

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

T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics New York University, Courant Institute of Mathematical Sciences, vol.10, 2003.

T. Cazenave and P. 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 : 10.1007/BF01403504

S. Cuccagna, Stabilization of solutions to nonlinear Schr??dinger equations, Communications on Pure and Applied Mathematics, vol.208, issue.1, pp.1110-1145, 2001.
DOI : 10.1002/cpa.1018

S. Cuccagna, ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS, Reviews in Mathematical Physics, vol.15, issue.08, pp.877-903, 2003.
DOI : 10.1142/S0129055X03001849

K. Datchev and I. Ventura, Solitary waves for the Hartree equation with a slowly varying potential, preprint

S. I. Dejak and I. M. Sigal, Long-time dynamics of KdV solitary waves over a variable bottom, Communications on Pure and Applied Mathematics, vol.20, issue.6, pp.869-905, 2006.
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E. Fermi, J. Pasta, and S. Ulam, Studies of nonlinear problems I, Los Alamos Report LA1940 (1955); reproduced in Nonlinear Wave Motion, Am. Math. Soc, pp.143-156, 1974.

J. C. Fernandez, C. Froesche, and G. Reinisch, Adiabatic Perturbations of Solitons and Shock Waves, Physica Scripta, vol.20, issue.3-4, pp.545-551, 1979.
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C. S. Gardner, M. D. Kruskal, and R. Miura, Korteweg-de Vries equation and generalizations . II. Existence of conservation laws and constants of motion, J. Math. Phys, vol.9, issue.8, pp.1204-1209, 1968.

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.1-71, 1979.
DOI : 10.1016/0022-1236(79)90076-4

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

M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry, II, Journal of Functional Analysis, vol.94, issue.2, pp.308-348, 1990.
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R. Grimshaw, Slowly Varying Solitary Waves. I. Korteweg-De Vries Equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.368, issue.1734, pp.359-375, 1979.
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R. Grimshaw, Slowly Varying Solitary Waves. II. Nonlinear Schrodinger Equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.368, issue.1734, pp.377-388, 1979.
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S. Gustafson, J. Fröhlich, B. L. Jonsson, and I. M. Sigal, Long time motion of NLS solitary waves in a confining potential, pp.621-660, 2006.

S. Gustafson, J. Fröhlich, B. L. Jonsson, and I. M. Sigal, Solitary wave dynamics in an external potential, Comm. Math. Phys, vol.250, pp.613-642, 2004.

R. Hirota, Exact Solution of the Korteweg???de Vries Equation for Multiple Collisions of Solitons, Physical Review Letters, vol.27, issue.18, pp.1192-1194, 1971.
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J. Holmer, Dynamics of KdV solitons in the presence of a slowly varying potential, preprint

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

URL : http://arxiv.org/abs/0709.0478

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

URL : http://arxiv.org/abs/math/0608510

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.
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URL : http://arxiv.org/abs/math/0602187

V. I. Karpman and E. M. Maslov, Perturbation theory for solitons, Soviet Phys, JETP Z. Eksper. Teoret. Fiz, vol.46, issue.2 2, pp.537-559, 1977.

D. J. Kaup and A. C. Newell, Solitons as Particles, Oscillators, and in Slowly Changing Media: A Singular Perturbation Theory, Proc. Roy. Soc. London Ser. A 361, pp.413-446, 1978.
DOI : 10.1098/rspa.1978.0110

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.
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K. Ko and H. H. , Korteweg-de Vries Soliton in a Slowly Varying Medium, Physical Review Letters, vol.40, issue.4, pp.233-236, 1978.
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M. D. Kruskal and N. J. Zabusky, Interaction of " solitons " in a collisionless plasma and recurrence of initial states, Phys. Rev. Lett, vol.15, pp.240-243, 1965.

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 : 10.1002/cpa.3160210503

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, Multi solitary waves for nonlinear Schrödinger equations, Ann. IHP Nonlinear Anal, vol.23, pp.849-864, 2006.

Y. Martel and F. Merle, Blow up in finite time and dynamics of blow up solutions for the L 2 -critical generalized KdV equation, Journal of the American Mathematical Society, vol.15, issue.03, pp.617-664, 2002.
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URL : https://hal.archives-ouvertes.fr/hal-00107235

Y. Martel and F. Merle, Description of two soliton collision for the quartic gKdV equations, preprint

Y. Martel and F. Merle, Stability of Two Soliton Collision for Nonintegrable gKdV Equations, Communications in Mathematical Physics, vol.15, issue.2, pp.39-79, 2009.
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URL : https://hal.archives-ouvertes.fr/hal-00408108

Y. Martel and F. Merle, Asymptotic stability of solitons of the subcritical gKdV equations revisited, Nonlinearity, vol.18, issue.1, pp.55-80, 2005.
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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.
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URL : https://hal.archives-ouvertes.fr/hal-00194565

Y. Martel and F. Merle, Description of the interaction of nearly equal solitons for the BBM equation, and Inelastic interaction of nearly equal solitons for the quartic gKdV equation, preprints

Y. Martel, F. Merle, and T. Mizumachi, Description of the Inelastic Collision of Two Solitary Waves for the BBM Equation, Archive for Rational Mechanics and Analysis, vol.15, issue.2
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Y. Martel, F. Merle, and T. Tsai, Stability and asymptotic stability in the energy pace of the sum of N solitons for subcritical gKdV equations, Comm. Math. Phys, pp.231-347, 2002.

Y. Martel, F. Merle, and T. Tsai, Stability in H 1 of the sum of K solitary waves for some nonlinear Schrödinger equations, Duke Math, Journal, vol.133, issue.3, pp.405-466, 2006.

F. Merle, Existence of blow-up solutions in the energy space for the critical generalized KdV equation, Journal of the American Mathematical Society, vol.14, issue.03, pp.555-578, 2001.
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C. Muñoz, On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity, International Mathematics Research Notices
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C. Muñoz, On the soliton dynamics under slowly varying medium for generalized Kortewegde Vries equations, preprint

C. Muñoz, On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations, preprint

C. Muñoz, On the soliton dynamics under slowly varying medium for gKdV equations: reflected solitons

C. Muñoz, On the soliton dynamics under slowly varying medium for NLS equations: reflected solitons

C. Muñoz, Lower bound on the defect at infinity for soliton-like solutions of slowly varying gKdV equations

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J. C. Bronski and R. L. Jerrard, Soliton dynamics in a potential, Mathematical Research Letters, vol.7, issue.3, pp.329-342, 2000.
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V. S. Buslaev and G. Perelman, Scattering for the nonlinear Schrödinger equation: states that are close to a soliton, St. Petersburg Math. J, vol.4, issue.6, pp.1111-1142, 1993.

T. Cazenave, Semilinear Schrödinger equations, Courant Lecture Notes in Mathematics New York University, Courant Institute of Mathematical Sciences, vol.10, 2003.

T. Cazenave and P. Lions, Orbital stability of standing waves for some nonlinear Schr???dinger equations, Communications in Mathematical Physics, vol.49, issue.4, pp.549-561, 1982.
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S. Cuccagna, Stabilization of solutions to nonlinear Schr??dinger equations, Communications on Pure and Applied Mathematics, vol.208, issue.1, pp.1110-1145, 2001.
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S. Cuccagna, ON ASYMPTOTIC STABILITY OF GROUND STATES OF NLS, Reviews in Mathematical Physics, vol.15, issue.08, pp.877-903, 2003.
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K. Datchev and I. Ventura, Solitary waves for the Hartree equation with a slowly varying potential, preprint

I. Dejak and B. L. Jonsson, Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves, Journal of Mathematical Physics, vol.47, issue.7, pp.72703-72719, 2006.
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C. S. Gardner, M. D. Kruskal, and R. Miura, Korteweg-de Vries equation and generalizations . II. Existence of conservation laws and constants of motion, J. Math. Phys, vol.9, issue.8, pp.1204-1209, 1968.

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.1-71, 1979.
DOI : 10.1016/0022-1236(79)90076-4

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

M. Grillakis, J. Shatah, and W. Strauss, Stability theory of solitary waves in the presence of symmetry, II, Journal of Functional Analysis, vol.94, issue.2, pp.308-348, 1990.
DOI : 10.1016/0022-1236(90)90016-E

R. Grimshaw, Slowly Varying Solitary Waves. I. Korteweg-De Vries Equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.368, issue.1734, pp.359-375, 1979.
DOI : 10.1098/rspa.1979.0135

R. Grimshaw, Slowly Varying Solitary Waves. II. Nonlinear Schrodinger Equation, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.368, issue.1734, pp.377-388, 1979.
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S. Gustafson, J. Fröhlich, B. L. Jonsson, and I. M. Sigal, Long time motion of NLS solitary waves in a confining potential, pp.621-660, 2006.

S. Gustafson, J. Fröhlich, B. L. Jonsson, and I. M. Sigal, Solitary wave dynamics in an external potential, Comm. Math. Phys, vol.250, pp.613-642, 2004.

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J. Holmer, Dynamics of KdV solitons in the presence of a slowly varying potential, preprint

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

URL : http://arxiv.org/abs/0709.0478

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

URL : http://arxiv.org/abs/math/0608510

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.
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D. J. Kaup and A. C. Newell, Solitons as Particles, Oscillators, and in Slowly Changing Media: A Singular Perturbation Theory, Proc. Roy. Soc. London Ser. A 361, pp.413-446, 1978.
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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.
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K. Ko and H. H. , Korteweg-de Vries Soliton in a Slowly Varying Medium, Physical Review Letters, vol.40, issue.4, pp.233-236, 1978.
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M. D. Kruskal and N. J. Zabusky, Interaction of " solitons " in a collisionless plasma and recurrence of initial states, Phys. Rev. Lett, vol.15, pp.240-243, 1965.

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Y. Martel and F. Merle, Multi solitary waves for nonlinear Schrödinger equations, Ann. IHP Nonlinear Anal, vol.23, pp.849-864, 2006.

Y. Martel and F. Merle, Blow up in finite time and dynamics of blow up solutions for the L 2 -critical generalized KdV equation, Journal of the American Mathematical Society, vol.15, issue.03, pp.617-664, 2002.
DOI : 10.1090/S0894-0347-02-00392-2

URL : https://hal.archives-ouvertes.fr/hal-00107235

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Y. Martel and F. Merle, Description of two soliton collision for the quartic gKdV equations, preprint

Y. Martel and F. Merle, Stability of Two Soliton Collision for Nonintegrable gKdV Equations, Communications in Mathematical Physics, vol.15, issue.2, pp.39-79, 2009.
DOI : 10.1007/s00220-008-0685-0

URL : https://hal.archives-ouvertes.fr/hal-00408108

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, 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, Description of the interaction of nearly equal solitons for the BBM equation, and Inelastic interaction of nearly equal solitons for the quartic gKdV equation, preprints

Y. Martel, F. Merle, and T. Mizumachi, Description of the Inelastic Collision of Two Solitary Waves for the BBM Equation, Archive for Rational Mechanics and Analysis, vol.15, issue.2
DOI : 10.1007/s00205-009-0244-7

URL : https://hal.archives-ouvertes.fr/hal-00408106

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

Y. Martel, F. Merle, and T. Tsai, Stability in H 1 of the sum of K solitary waves for some nonlinear Schrödinger equations, Duke Math, Journal, vol.133, issue.3, pp.405-466, 2006.

F. Merle, Existence of blow-up solutions in the energy space for the critical generalized KdV equation, Journal of the American Mathematical Society, vol.14, issue.03, pp.555-578, 2001.
DOI : 10.1090/S0894-0347-01-00369-1

R. M. Miura, The Korteweg???deVries Equation: A Survey of Results, SIAM Review, vol.18, issue.3, pp.412-459, 1976.
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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.
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C. Muñoz, On the Inelastic Two-Soliton Collision for gKdV Equations with General Nonlinearity, International Mathematics Research Notices
DOI : 10.1093/imrn/rnp204

C. Muñoz, On the soliton dynamics under slowly varying medium for generalized Kortewegde Vries equations, preprint

C. Muñoz, On the soliton dynamics under slowly varying medium for Nonlinear Schrödinger equations, preprint

C. Muñoz, On the soliton dynamics under slowly varying medium for gKdV equations: reflected solitons

C. Muñoz, On the soliton dynamics under slowly varying medium for NLS equations: reflected solitons

C. Muñoz, Lower bound on the defect at infinity for soliton-like solutions of slowly varying gKdV equations

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