New integrable multi-component NLS type equations on symmetric spaces:
reductions. (English) Zbl 1101.35070
Mladenov, Ivaïlo (ed.) et al., Proceedings of the 7th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 2–10, 2005. Sofia: Bulgarian Academy of Sciences (ISBN 954-8495-30-9/pbk). 154-175 (2006).
Summary: The reductions of the multi-component nonlinear Schrödinger models related to C.I and D.III type symmetric spaces are studied. We pay special attention to the MNLS related to the , and Lie algebras. The MNLS related to is a three-component MNLS which finds applications to Bose-Einstein condensates. The MNLS related to and Lie algebras after convenient or reductions reduce to three and four-component MNLS showing new types of -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 and the corresponding recursion operator are outlined. Applications to spinor model of Bose-Einstein condensates are discussed.
|35Q55||NLS-like (nonlinear Schrödinger) equations|
|37K30||Relations of infinite-dimensional systems with algebraic structures|
|82B10||Quantum equilibrium statistical mechanics (general)|