Bose-Einstein condensates with F=1 and F=2. Reductions and soliton interactions of multi-component NLS models

We analyze a class of multicomponent nonlinear Schrodinger equations (MNLS) related to the symmetric BD.I-type symmetric spaces and their reductions. We briefly outline the direct and the inverse scattering method for the relevant Lax operators and the soliton solutions. We use the Zakharov-Shabat dressing method to obtain the two-soliton solution and analyze the soliton interactions of the MNLS equations and some of their reductions.

Solutions of multi-component NLS models and spinor Bose-Einstein condensates

A three- and five-component nonlinear Schrodinger-type models, which describe spinor Bose-Einstein condensates (BECs) with hyperfine structures F=1 and F=2 respectively, are studied. These models for particular values of the coupling constants are integrable by the inverse scattering method. They are related to symmetric spaces of BD.I-type SO(2r+1)/(SO(2) x SO(2r-1)) for r=2 and r=3. Using conveniently modified Zakharov-Shabat dressing procedure we obtain different types of soliton solutions.

How many types of soliton solutions do we know?

We consider several ways of how one could classify the various types of soliton solutions related to nonlinear evolution equations which are solvable by the inverse scattering method. In doing so we make use of the fundamental analytic solutions, the dressing procedure, the reduction technique and other tools characteristic for that method.