Soliton dynamics for CNLS systems with potentials

Asymptotic Analysis (Impact Factor: 0.53). 10/2008; 66(2). DOI: 10.3233/ASY-2009-0959
Source: arXiv


The semiclassical limit of a weakly coupled nonlinear focusing Schrödinger system in presence of a nonconstant potential is studied. The initial data is of the x−˜x i form (u1, u2) with ui = ri ε e ε x· ˜ ξ, where (r1, r2) is a real ground state solution, belonging to a suitable class, of an associated autonomous elliptic system. For ε sufficiently small, the solution (φ1, φ2) will been shown to have, locally in time, the x−x(t)) i form (r1 ε e ε x·ξ(t) ( x−x(t)) i, r2 ε e ε x·ξ(t)), where (x(t), ξ(t)) is the solution of the Hamiltonian system ˙x(t) = ξ(t), ξ(t) ˙ = −∇V (x(t)) with x(0) = ˜x and ξ(0) = ξ.

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Available from: Marco Squassina, Jan 04, 2013
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