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

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

2007-10-17

arxiv.org/abs/0710.3302v1

J. Nonlin. Math. Phys. 15 (2008), suppl.3, 197 - 208

Nonlinear Sciences

Exactly Solvable and Integrable Systems

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

Scientific paper

10.2991/jnmp.2008.15.s3.20

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.

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