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A faithful symbolic extension
On asymptotic stability of solitons in a nonlinear Schrödinger equation
1. | Faculty of Mathematics of Vienna University, Vienna, Australia |
2. | IITP RAS, Moscow, Russian Federation |
3. | Centre for Mathematical Sciences, Cambridge, United Kingdom |
References:
[1] |
V. Buslaev, A. Komech, E. Kopylova and D. Stuart, On asymptotic stability of solitary waves in a nonlinear Schrödinger equation, Comm. Partial Diff. Eqns., \textbf{33} (2008), 669-705.
doi: 10.1080/03605300801970937. |
[2] |
V. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 20 (2003), 419-475.
doi: 10.1016/S0294-1449(02)00018-5. |
[3] |
A. I. Komech and A. A. Komech, Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator, Russ. J. Math. Phys., 14 (2007), 164-173.
doi: 10.1134/S1061920807020057. |
[4] |
A. Komech and E.Kopylova, On Asymptotic stability of moving kink for relativistic Ginsburg-Landau equation, Commun. Math. Phys., 302 (2011), 225-252.
doi: 10.1007/s00220-010-1184-7. |
[5] |
A. Komech, E. Kopylova and D. Stuart, On asymptotic stability of solitons for nonlinear Schrödinger equation,, preprint, ().
|
[6] |
M. Merkli and I. M. Sigal, A time-dependent theory of quantum resonances, Commun. Math. Phys., 201 (1999), 549-576.
doi: 10.1007/s002200050568. |
[7] |
R. L. Pego and M. I. Weinstein, Asymptotic stability of solitary waves, Commun. Math. Phys., 164 (1994), 305-349.
doi: 10.1007/BF02101705. |
[8] |
C. A. Pillet and C. E. Wayne, Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations, J. Diff. Eqns, 141 (1997), 310-326.
doi: 10.1006/jdeq1997.3345. |
[9] |
A. Soffer and M. I. Weinstein, Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math., 136 (1999), 9-74.
doi: 10.1007/s002220050303. |
[10] |
A. Soffer and M. I. Weinstein, Selection of the ground state for nonlinear Schrodinger equations, Rev. Math. Phys., 16 (2004), 977-1071.
doi: 10.1142/S0129055X04002175. |
show all references
References:
[1] |
V. Buslaev, A. Komech, E. Kopylova and D. Stuart, On asymptotic stability of solitary waves in a nonlinear Schrödinger equation, Comm. Partial Diff. Eqns., \textbf{33} (2008), 669-705.
doi: 10.1080/03605300801970937. |
[2] |
V. Buslaev and C. Sulem, On asymptotic stability of solitary waves for nonlinear Schrödinger equations, Ann. Inst. Henri Poincaré, Anal. Non Linéaire, 20 (2003), 419-475.
doi: 10.1016/S0294-1449(02)00018-5. |
[3] |
A. I. Komech and A. A. Komech, Global well-posedness for the Schrödinger equation coupled to a nonlinear oscillator, Russ. J. Math. Phys., 14 (2007), 164-173.
doi: 10.1134/S1061920807020057. |
[4] |
A. Komech and E.Kopylova, On Asymptotic stability of moving kink for relativistic Ginsburg-Landau equation, Commun. Math. Phys., 302 (2011), 225-252.
doi: 10.1007/s00220-010-1184-7. |
[5] |
A. Komech, E. Kopylova and D. Stuart, On asymptotic stability of solitons for nonlinear Schrödinger equation,, preprint, ().
|
[6] |
M. Merkli and I. M. Sigal, A time-dependent theory of quantum resonances, Commun. Math. Phys., 201 (1999), 549-576.
doi: 10.1007/s002200050568. |
[7] |
R. L. Pego and M. I. Weinstein, Asymptotic stability of solitary waves, Commun. Math. Phys., 164 (1994), 305-349.
doi: 10.1007/BF02101705. |
[8] |
C. A. Pillet and C. E. Wayne, Invariant manifolds for a class of dispersive, Hamiltonian, partial differential equations, J. Diff. Eqns, 141 (1997), 310-326.
doi: 10.1006/jdeq1997.3345. |
[9] |
A. Soffer and M. I. Weinstein, Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math., 136 (1999), 9-74.
doi: 10.1007/s002220050303. |
[10] |
A. Soffer and M. I. Weinstein, Selection of the ground state for nonlinear Schrodinger equations, Rev. Math. Phys., 16 (2004), 977-1071.
doi: 10.1142/S0129055X04002175. |
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