Asymptotic stability of solitary waves for nonlinear Schrödinger equations
Séminaire Équations aux dérivées partielles (Polytechnique) (2002-2003), Talk no. 8, 15 p.
@article{SEDP_2002-2003____A8_0,
     author = {Perelman, Galina},
     title = {Asymptotic stability of solitary waves for nonlinear Schr\"odinger equations},
     journal = {S\'eminaire \'Equations aux d\'eriv\'ees partielles (Polytechnique)},
     publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique},
     year = {2002-2003},
     note = {talk:8},
     mrnumber = {2030703},
     zbl = {1062.35139},
     language = {en},
     url = {http://www.numdam.org/item/SEDP_2002-2003____A8_0}
}
Perelman, Galina. Asymptotic stability of solitary waves for nonlinear Schrödinger equations. Séminaire Équations aux dérivées partielles (Polytechnique) (2002-2003), Talk no. 8, 15 p. http://www.numdam.org/item/SEDP_2002-2003____A8_0/

[1] Berestycki, H.; Lions, P.-L. Nonlinear scalar field equations, I, II, Arch. Rat. Mech. Anal. 1983, 82 (4), 313-375. | MR 695535 | Zbl 0533.35029

[2] Buslaev V.S.; Perelman, G.S. Scattering for the nonlinear Schrödinger equation: states close to a soliton. St. Petersburg Math. J. 1993, 4 (6),1111-1143. | MR 1199635 | Zbl 0853.35112

[3] Cuccagna, S. Stabilization of solutions to nonlinear Schrödinger equation, Comm. Pure Appl. Math. 2001 54, 1110-1145. | MR 1835384 | Zbl 1031.35129

[4] Ginibre, J.; Velo G. On a class of nonlinear Schrödinger equations I, II. J.Func.Anal. 1979, 32, 1-71. | MR 533219 | Zbl 0396.35029

[5] Ginibre, J.; Velo G. On a class of nonlinear Schrödinger equations III. Ann. Inst. H.Poincare -Phys. Theor. 1978, 28 (3), 287-316. | Numdam | MR 498408 | Zbl 0397.35012

[6] Hagedorn, G. Asymptotic completeness for the impact parameter approximation to three particle scattering. Ann. Inst. Henri Poincaré. 1982, 36 (1), 19-40. | Numdam | MR 653016 | Zbl 0482.47003

[7] McLeod, K. Uniqueness of positive radial solutions of u+f(u)=0 in n . Trans. Amer. Math. Soc. 1993, 339 (2), 495-505. | MR 1201323 | Zbl 0804.35034

[8] Nier, F.; Soffer, A. Dispersion and Strichartz estimates for some finite rank perturbations of the Laplace operator. J. of Func. Analysis, to appear. | MR 1964550 | Zbl 1034.35017

[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. | MR 1608275 | Zbl 0931.35164

[10] Perelman, G. Asymptotic stability of solitons for nonlinear Schrödinger equations, preprint. | Zbl 1067.35113

[11] Soffer A.; Weinstein, M.I. Multichannel nonlinear scattering theory for nonintegrable equations I. Commun. Math. Phys. 1990, 133 (1), 119-146. | MR 1071238 | Zbl 0721.35082

[12] Soffer A.; Weinstein, M.I. Multichannel nonlinear scattering theory for nonintegrable equations II. J. Diff. Eq. 1992, 98 (2), 376-390. | MR 1170476 | Zbl 0795.35073

[13] Weinstein, M.I. Modulation stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 1985, 16 (3), 472-491. | MR 783974 | Zbl 0583.35028

[14] Weinstein, M.I. Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math. 1986, 39 (1), 51-68. | MR 820338 | Zbl 0594.35005