On asymptotic stability of solitary waves for nonlinear Schrödinger equations

Vladimir S. Buslaev; Catherine Sulem

Annales de l'I.H.P. Analyse non linéaire (2003)

  • Volume: 20, Issue: 3, page 419-475
  • ISSN: 0294-1449

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Buslaev, Vladimir S., and Sulem, Catherine. "On asymptotic stability of solitary waves for nonlinear Schrödinger equations." Annales de l'I.H.P. Analyse non linéaire 20.3 (2003): 419-475. <http://eudml.org/doc/78586>.

@article{Buslaev2003,
author = {Buslaev, Vladimir S., Sulem, Catherine},
journal = {Annales de l'I.H.P. Analyse non linéaire},
keywords = {nonlinear Schrödinger equations; solitary waves; asymptotic stability},
language = {eng},
number = {3},
pages = {419-475},
publisher = {Elsevier},
title = {On asymptotic stability of solitary waves for nonlinear Schrödinger equations},
url = {http://eudml.org/doc/78586},
volume = {20},
year = {2003},
}

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
PB - Elsevier
VL - 20
IS - 3
SP - 419
EP - 475
LA - eng
KW - nonlinear Schrödinger equations; solitary waves; asymptotic stability
UR - http://eudml.org/doc/78586
ER -

References

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  3. [3] Buslaev V., Perelman G., On the stability of solitary waves for nonlinear Schrödinger equations, Amer. Math. Soc. Transl.164 (1995) 75-98. Zbl0841.35108MR1334139
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  7. [7] Grikurov V.E., Perturbation of unstable solitons for generalized NLS with saturating nonlinearity, in: Intern. Seminar ‘Day on Diffraction-97’, 1997, pp. 170-179. 
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  12. [12] Soffer A., Weinstein M., Multichannel nonlinear scattering for non-integrable equations, Comm. Math. Phys.133 (1990) 119-146. Zbl0721.35082MR1071238
  13. [13] Soffer A., Weinstein M., Resonances, radiation damping and instability in Hamiltonian nonlinear wave equations, Invent. Math.136 (1999) 9-74. Zbl0910.35107MR1681113
  14. [14] Strauss W., Nonlinear scattering theory at low energy, J. Funct. Anal.41 (1981) 110-133, J. Funct. Anal.43 (1981) 281-293. Zbl0466.47006MR614228
  15. [15] C. Sulem, P.-L. Sulem, The Nonlinear Schrödinger Equation: Self-focusing and Wave Collapse, in: Applied Mathematical Sciences, Vol. 139, Springer. Zbl0928.35157MR1696311
  16. [16] Weinstein M., Lyapunov stability of ground states of nonlinear dispersive evolution equations, Comm. Pure Appl. Math.39 (1986) 51-68. Zbl0594.35005MR820338
  17. [17] Yau H.-T., Tsai T.-P., Asymptotic dynamics of nonlinear Schrödinger equations: resonance dominated and radiation dominated solutions, Comm. Pure Appl. Math.LV (2002) 1-64. Zbl1031.35137MR1865414

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