630 research outputs found
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.Comment: SPIE UNO-09-UN101-19, SPIE Volume: 7501, (2009
Fordy-Kulish models and spinor Bose-Einstein condensates
A three-component nonlinear Schrodinger-type model which describes spinor
Bose-Einstein condensate (BEC) is considered. This model is integrable by the
inverse scattering method and using Zakharov-Shabat dressing method we obtain
three types of soliton solutions. The multi-component nonlinear Schrodinger
type models related to symmetric spaces C.I Sp(4)/U(2) is studied.Comment: 8 pages, LaTeX, jnmp styl
New Integrable Multi-Component NLS Type Equations on Symmetric Spaces: Z_4 and Z_6 Reductions
The reductions of the multi-component nonlinear Schrodinger (MNLS) type
models related to C.I and D.III type symmetric spaces are studied. We pay
special attention to the MNLS related to the sp(4), so(10) and so(12) Lie
algebras. The MNLS related to sp(4) is a three-component MNLS which finds
applications to Bose-Einstein condensates. The MNLS related to so(12) and
so(10) Lie algebras after convenient Z_6 or Z_4 reductions reduce to three and
four-component MNLS showing new types of chi ^(3)-interactions that are
integrable. We briefly explain how these new types of MNLS can be integrated by
the inverse scattering method. The spectral properties of the Lax operators L
and the corresponding recursion operator Lambda are outlined. Applications to
spinor model of Bose-Einstein condensates are discussed.Comment: Reported to the Seventh International conference "Geometry,
Integrability and Quantization", June 2--10, 2005, Varna, Bulgari
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