The generalised Zakharov-Shabat system and the gauge group action

Georgi G. Grahovski

Research output: Contribution to journalArticlepeer-review

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 languageEnglish
Article number073512
Pages (from-to)073512-073512-13
JournalJournal of Mathematical Physics
Volume53
Issue number7
DOIs
Publication statusPublished - 12 Jul 2012
Externally publishedYes

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

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