On soliton dynamics in nonlinear Schrödinger equations. (English) Zbl 1110.35084

Gang, Zhou; Sigal, I. M.

Geom. Funct. Anal. 16, No. 6, 1377-1390 (2006).

From the summary: We describe our results on dynamics of solitons in generalized nonlinear Schrödinger equations with external potentials in all dimensions except for 2. We also outline some of the ideas of the proofs involved. The detailed discussion of the results as well as the proofs are presented in [Zhou Gang and I. M. Sigal, Relaxation to trapped solitons in nonlinear Schrödinger equations with potential, submitted].

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
35Q51	Soliton equations
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Keywords:

asymptotic stability; relaxation to the ground state; Gross-Pitaevskii equation; Bose-Einstein condensation