Slow solution interaction with delta imperiums. (English) Zbl 1137.35060

Holmer, Justin; Zworski, Maciej

J. Mod. Dyn. 1, No. 4, 689-718 (2007).

The Gross-Pitaevskii equation with a delta function as a potential is under consideration. The initial condition is a soliton. The case when modulus of small amplitude of potential is not less than square of initial velocity is analysed.

Reviewer: Igor Andrianov (Köln)

MSC:

35Q53	KdV equations (Korteweg-de Vries equations)
35Q55	NLS equations (nonlinear Schrödinger equations)
37K40	Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems

Keywords:

soliton; effective Hamiltonian; Gross-Pitaevskii equation; nonlinear Schrödinger equation; Dirac mass potential