Soliton dynamics for CNLS systems with potentials

Asymptotic Analysis (Impact Factor: 0.42). 10/2008;
Source: arXiv

ABSTRACT The soliton dynamics in the semiclassical limit for a weakly coupled nonlinear focusing Schr\"odinger systems in presence of a nonconstant potential is studied by taking as initial data some rescaled ground state solutions of an associate elliptic system. Comment: 25 pages, 2 figures

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    ABSTRACT: The soliton dynamics for a general class of nonlinear focusing Schrödinger problems in presence of non-constant external (local and nonlocal) potentials is studied by taking as initial datum the ground state solution of an associated autonomous elliptic equation.
    Journal of Mathematical Analysis and Applications 05/2010; 365:776-796. DOI:10.1016/j.jmaa.2009.11.045 · 1.12 Impact Factor
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    ABSTRACT: We study blow-up, global existence and ground state solutions for the N-coupled focusing nonlinear Schrödinger equations. Firstly, using the Nehari manifold approach and some variational techniques, the existence of ground state solutions to the equations (CNLS) is established. Secondly, under certain conditions, finite time blow-up phenomena of the solutions is derived. Finally, by introducing a refined version of compactness lemma, the L 2 concentration for the blow-up solutions is obtained.
    Acta Mathematica Sinica 07/2014; 30(7):1161-1179. DOI:10.1007/s10114-014-3314-1 · 0.42 Impact Factor
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    ABSTRACT: We study the behavior of the soliton solutions of the equation i((\partial{\psi})/(\partialt))=-(1/(2m)){\Delta}{\psi}+(1/2)W_{{\epsilon}}'({\psi})+V(x){\psi} where W_{{\epsilon}}' is a suitable nonlinear term which is singular for {\epsilon}=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 {\epsilon}\to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).
    Archive for Rational Mechanics and Analysis 04/2011; 205(2). DOI:10.1007/s00205-012-0510-y · 2.02 Impact Factor

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