On the Caudrey-Beals-Coifman System and the Gauge Group Action

Abstract

The generalized Zakharov-Shabat systems with complex-valued Cartan elements and the systems studied by Caudrey, Beals and Coifman (CBC systems) and their gauge equivalent are studies. This includes: the properties of fundamental analytical solutions (FAS) 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.

arXiv comment12 pages, no figures, contribution to the NEEDS 2007 proceedings (Submitted to J. Nonlin. Math. Phys.)

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Cited by in corpus (7)

• Inverse Scattering Transform for the Degasperis-Procesi Equation
• On the N-wave Equations with PT-symmetry
• Nonlocal reductions of the Ablowitz-Ladik equation
• On nonlocal reductions of the multi-component nonlinear Schrodinger equation on symmetric spaces
• The Generalised Zakharov-Shabat System and the Gauge Group Action
• Real Hamiltonian forms of affine Toda field theories: spectral aspects
• On the $N$-waves hierarchy with constant boundary conditions. Spectral properties