Abstract
The generalized Zakharov-Shabat systems with complex-valued non-regular Cartan elements and the systems studied by Caudrey, Beals, and Coifman (CBC) systems and their gauge equivalent are studied. This study includes: the properties of fundamental analytical solutions for the gauge equivalent to CBC systems and the minimal set of scattering data; the description of the class of nonlinear evolutionary equations, solvable by the inverse scattering method, and the recursion operator, related to such systems; the hierarchies of Hamiltonian structures. The results are illustrated in the example of the multi-component nonlinear Schrödinger equations and the corresponding gauge-equivalent multi-component Heisenberg ferromagnetic type models, related to so(5,C{double-struck}) algebra.
Original language | English |
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Article number | 073512 |
Pages (from-to) | 073512-073512-13 |
Journal | Journal of Mathematical Physics |
Volume | 53 |
Issue number | 7 |
DOIs | |
Publication status | Published - 12 Jul 2012 |
Externally published | Yes |
Keywords
- generalized Zakharov–Shabat systems
- complex-valued non-regular Cartan elements
- Caudrey, Beals and Coifman (CBC) systems
- gauge equivalent
- fundamental analytical solutions (FAS)
- minimal set of scattering data
- nonlinear evolutionary equations
- inverse scattering method
- recursion operator
- hierarchies of Hamiltonian structures
- multi-component nonlinear Schrödinger (MNLS) equations
- multi-component Heisenberg ferromagnetic (MHF) type models
- so(5,C) algebra