On the Dynamics of solitons in the nonlinear Schroedinger equation
arXiv:1104.3989 · doi:10.1007/s00205-012-0510-y
Abstract
We study the behavior of the soliton solutions of the equation i((\partialψ)/(\partialt))=-(1/(2m))Δψ+(1/2)W_{ε}'(ψ)+V(x)ψ where W_{ε}' is a suitable nonlinear term which is singular for ε=0. We use the "strong" nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for ε\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).
29 pages
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Cited by in corpus (5)
- Multiplicity and concentration results for local and fractional NLS equations with critical growth
- Soliton dynamics for the generalized Choquard equation
- Multi-soliton dynamics in the nonlinear Schrödinger equation
- Existence and stability results on a class of Non Linear Schroedinger Equations in bounded domains with Dirichlet boundary conditions
- Soliton dynamics for fractional Schrodinger equations