Asymptotic stability of solitary waves for nonlinear Schrödinger equations

Galina Perelman

Séminaire Équations aux dérivées partielles (2002-2003)

  • Volume: 2002-2003, page 1-15

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Perelman, Galina. "Asymptotic stability of solitary waves for nonlinear Schrödinger equations." Séminaire Équations aux dérivées partielles 2002-2003 (2002-2003): 1-15. <http://eudml.org/doc/11074>.

@article{Perelman2002-2003,
author = {Perelman, Galina},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {nonlinear Schrödinger equation; soliton; asymptotic stability; large time asymptotics},
language = {eng},
pages = {1-15},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Asymptotic stability of solitary waves for nonlinear Schrödinger equations},
url = {http://eudml.org/doc/11074},
volume = {2002-2003},
year = {2002-2003},
}

TY - JOUR
AU - Perelman, Galina
TI - Asymptotic stability of solitary waves for nonlinear Schrödinger equations
JO - Séminaire Équations aux dérivées partielles
PY - 2002-2003
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 2002-2003
SP - 1
EP - 15
LA - eng
KW - nonlinear Schrödinger equation; soliton; asymptotic stability; large time asymptotics
UR - http://eudml.org/doc/11074
ER -

References

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  3. Cuccagna, S. Stabilization of solutions to nonlinear Schrödinger equation, Comm. Pure Appl. Math. 200154, 1110-1145. Zbl1031.35129MR1835384
  4. Ginibre, J.; Velo G. On a class of nonlinear Schrödinger equations I, II. J.Func.Anal. 1979, 32, 1-71. Zbl0396.35029MR533219
  5. Ginibre, J.; Velo G. On a class of nonlinear Schrödinger equations III. Ann. Inst. H.Poincare -Phys. Theor. 1978, 28 (3), 287-316. Zbl0397.35012MR498408
  6. Hagedorn, G. Asymptotic completeness for the impact parameter approximation to three particle scattering. Ann. Inst. Henri Poincaré. 1982, 36 (1), 19-40. Zbl0482.47003MR653016
  7. McLeod, K. Uniqueness of positive radial solutions of ▵ u + f ( u ) = 0 in ℝ n . Trans. Amer. Math. Soc. 1993, 339 (2), 495-505. Zbl0804.35034MR1201323
  8. Nier, F.; Soffer, A. Dispersion and Strichartz estimates for some finite rank perturbations of the Laplace operator. J. of Func. Analysis, to appear. Zbl1034.35017MR1964550
  9. Perelman, G. Some results on the scattering of weakly interacting solitons for nonlinear Schrödinger equation. In: Spectral Theory, Microlocal Analysis, Singular Manifolds, M.Demuth et al., eds., Math. Top. 14, Berlin, Akademie Verlag, 1997, pp. 78-137. Zbl0931.35164MR1608275
  10. Perelman, G. Asymptotic stability of solitons for nonlinear Schrödinger equations, preprint. Zbl1067.35113
  11. Soffer A.; Weinstein, M.I. Multichannel nonlinear scattering theory for nonintegrable equations I. Commun. Math. Phys. 1990, 133 (1), 119-146. Zbl0721.35082MR1071238
  12. Soffer A.; Weinstein, M.I. Multichannel nonlinear scattering theory for nonintegrable equations II. J. Diff. Eq. 1992, 98 (2), 376-390. Zbl0795.35073MR1170476
  13. Weinstein, M.I. Modulation stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 1985, 16 (3), 472-491. Zbl0583.35028MR783974
  14. Weinstein, M.I. Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math. 1986, 39 (1), 51-68. Zbl0594.35005MR820338

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