@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) dit aussi "S\'eminaire Goulaouic-Schwartz"}, note = {talk:8}, pages = {1--15}, publisher = {Centre de math\'ematiques Laurent Schwartz, \'Ecole polytechnique}, year = {2002-2003}, zbl = {1062.35139}, mrnumber = {2030703}, language = {en}, url = {http://archive.numdam.org/item/SEDP_2002-2003____A8_0/} }
TY - JOUR AU - Perelman, Galina TI - Asymptotic stability of solitary waves for nonlinear Schrödinger equations JO - Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" N1 - talk:8 PY - 2002-2003 SP - 1 EP - 15 PB - Centre de mathématiques Laurent Schwartz, École polytechnique UR - http://archive.numdam.org/item/SEDP_2002-2003____A8_0/ LA - en ID - SEDP_2002-2003____A8_0 ER -
%0 Journal Article %A Perelman, Galina %T Asymptotic stability of solitary waves for nonlinear Schrödinger equations %J Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" %Z talk:8 %D 2002-2003 %P 1-15 %I Centre de mathématiques Laurent Schwartz, École polytechnique %U http://archive.numdam.org/item/SEDP_2002-2003____A8_0/ %G en %F SEDP_2002-2003____A8_0
Perelman, Galina. Asymptotic stability of solitary waves for nonlinear Schrödinger equations. Séminaire Équations aux dérivées partielles (Polytechnique) dit aussi "Séminaire Goulaouic-Schwartz" (2002-2003), Talk no. 8, 15 p. http://archive.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 | Zbl
[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 | Zbl
[3] Cuccagna, S. Stabilization of solutions to nonlinear Schrödinger equation, Comm. Pure Appl. Math. 2001 54, 1110-1145. | MR | Zbl
[4] Ginibre, J.; Velo G. On a class of nonlinear Schrödinger equations I, II. J.Func.Anal. 1979, 32, 1-71. | MR | Zbl
[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 | Zbl
[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 | Zbl
[7] McLeod, K. Uniqueness of positive radial solutions of in . Trans. Amer. Math. Soc. 1993, 339 (2), 495-505. | MR | Zbl
[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 | Zbl
[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 | Zbl
[10] Perelman, G. Asymptotic stability of solitons for nonlinear Schrödinger equations, preprint. | Zbl
[11] Soffer A.; Weinstein, M.I. Multichannel nonlinear scattering theory for nonintegrable equations I. Commun. Math. Phys. 1990, 133 (1), 119-146. | MR | Zbl
[12] Soffer A.; Weinstein, M.I. Multichannel nonlinear scattering theory for nonintegrable equations II. J. Diff. Eq. 1992, 98 (2), 376-390. | MR | Zbl
[13] Weinstein, M.I. Modulation stability of ground states of nonlinear Schrödinger equations. SIAM J. Math. Anal. 1985, 16 (3), 472-491. | MR | Zbl
[14] Weinstein, M.I. Lyapunov stability of ground states of nonlinear dispersive evolution equations. Comm. Pure Appl. Math. 1986, 39 (1), 51-68. | MR | Zbl