@article{AIHPC_2003__20_3_419_0, author = {Buslaev, Vladimir S. and Sulem, Catherine}, title = {On asymptotic stability of solitary waves for nonlinear {Schr\"odinger} equations}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {419--475}, publisher = {Elsevier}, volume = {20}, number = {3}, year = {2003}, doi = {10.1016/S0294-1449(02)00018-5}, mrnumber = {1972870}, zbl = {1028.35139}, language = {en}, url = {http://archive.numdam.org/articles/10.1016/S0294-1449(02)00018-5/} }
TY - JOUR AU - Buslaev, Vladimir S. AU - Sulem, Catherine TI - On asymptotic stability of solitary waves for nonlinear Schrödinger equations JO - Annales de l'I.H.P. Analyse non linéaire PY - 2003 SP - 419 EP - 475 VL - 20 IS - 3 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/S0294-1449(02)00018-5/ DO - 10.1016/S0294-1449(02)00018-5 LA - en ID - AIHPC_2003__20_3_419_0 ER -
%0 Journal Article %A Buslaev, Vladimir S. %A Sulem, Catherine %T On asymptotic stability of solitary waves for nonlinear Schrödinger equations %J Annales de l'I.H.P. Analyse non linéaire %D 2003 %P 419-475 %V 20 %N 3 %I Elsevier %U http://archive.numdam.org/articles/10.1016/S0294-1449(02)00018-5/ %R 10.1016/S0294-1449(02)00018-5 %G en %F AIHPC_2003__20_3_419_0
Buslaev, Vladimir S.; Sulem, Catherine. On asymptotic stability of solitary waves for nonlinear Schrödinger equations. Annales de l'I.H.P. Analyse non linéaire, Volume 20 (2003) no. 3, pp. 419-475. doi : 10.1016/S0294-1449(02)00018-5. http://archive.numdam.org/articles/10.1016/S0294-1449(02)00018-5/
[1] Orbital stability of standing waves for some nonlinear Schrödinger equations, Comm. Math. Phys. 85 (1982) 549-561. | MR | Zbl
, ,[2] Scattering for the nonlinear Schrödinger equation: states close to a soliton, St. Petersburg Math. J. 4 (1993) 1111-1142. | MR | Zbl
, ,[3] On the stability of solitary waves for nonlinear Schrödinger equations, Amer. Math. Soc. Transl. 164 (1995) 75-98. | MR | Zbl
, ,[4] Stabilization of solutions to nonlinear Schrödinger equations, Comm. Pure Appl. Math. LIV (2001) 1110-1145. | MR | Zbl
,[5] P. Deift, X. Zhou, Perturbation theory for infinite dimensional integrable systems on the line, Preprint.
[6] On a class of Schrödinger equations. I: The Cauchy problem, General case; II: Scattering theory, General case, J. Funct. Anal. 32 (1979) 1-32, 33-71. | MR | Zbl
, ,[7] Perturbation of unstable solitons for generalized NLS with saturating nonlinearity, in: Intern. Seminar ‘Day on Diffraction-97', 1997, pp. 170-179.
,[8] Stability theory of solitary waves in the presence of symmetry, Part I, J. Funct. Anal. 74 (1987) 160-197. | MR | Zbl
, , ,[9] The nonlinear Schrödinger equation and the nonlinear heat equation reduction to linear form, Comm. Pure Appl. Math. 44 (1991) 1067-1083. | MR | Zbl
, ,[10] On the formation of singularities in solutions of the critical nonlinear Schrödinger equation, Ann. Inst. Henri Poincaré 2 (2001) 605-673. | MR | Zbl
,[11] Internal modes of envelope solitons, Phys. D 116 (1998) 121-142. | MR | Zbl
, , ,[12] Multichannel nonlinear scattering for non-integrable equations, Comm. Math. Phys. 133 (1990) 119-146. | MR | Zbl
, ,[13] Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math. 136 (1999) 9-74. | MR | Zbl
, ,[14] Nonlinear scattering theory at low energy, J. Funct. Anal. 41 (1981) 110-133, J. Funct. Anal. 43 (1981) 281-293. | MR | Zbl
,[15] C. Sulem, P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse, in: Applied Mathematical Sciences, Vol. 139, Springer. | MR | Zbl
[16] Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math. 39 (1986) 51-68. | MR | Zbl
,[17] Asymptotic dynamics of nonlinear Schrödinger equations: resonance dominated and radiation dominated solutions, Comm. Pure Appl. Math. LV (2002) 1-64. | MR | Zbl
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