Asymptotic stability and completeness in the energy space for nonlinear Schrödinger equations with small solitary waves. (English) Zbl 1072.35167

Gustafson, Stephen; Nakanishi, Kenji; Tsai, Tai-Peng

Int. Math. Res. Not. 2004, No. 66, 3559-3584 (2004).

Small in \(H^1\) solutions are decomposed into solitary and dispersive waves. It is shown that as \(t \rightarrow \infty\), the solitary wave component converges to a fixed solitary wave, and the dispersive component converges strongly in \(H^1\) to a solution of the free Schrödinger equation.

Reviewer: Igor Andrianov (Köln)

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35B35	Stability in context of PDEs
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
37K45	Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems
35Q51	Soliton equations

Keywords:

NLS equation; soliton; dispersive wave; asymptotic stability; asymptotic completeness