paper

Bose-Einstein Condensates and spectral properties of multicomponent nonlinear Schrodinger equations

arXiv:1001.0164

Abstract

We analyze the properties of the soliton solutions of a class of models describing one-dimensional BEC with spin F. We describe the minimal sets of scattering data which determine uniquely both the corresponding potential of the Lax operator and its scattering matrix. Next we give several reductions of these MNLS, derive their N-soliton solutions and analyze the soliton interactions. Finally we prove an important theorem proving that if the initial conditions satisfy the reduction then one gets a solution of the reduced MNLS.

Submitted to Discrete and Continuous Dynamical Systems B, special volume of LENCOS conference, July 14-17, Seville

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