Locality of the conservation laws for the soliton equations related to Caudrey-Beals-Coifman system. (English) Zbl 1305.35125

Yanovski, Alexandar

J. Geom. Symmetry Phys. 33, 91-107 (2014).

Summary: We consider the hierarchies of nonlinear evolution equations related to auxiliary problem of Caudrey-Beals-Coifman type. We give a proof that the conservation laws for these equations have local densities based on the theory of the generating operators related to the Caudrey-Beals-Coifman linear problem.

MSC:

35Q51	Soliton equations
37K30	Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with infinite-dimensional Lie algebras and other algebraic structures
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
35L65	Hyperbolic conservation laws

Keywords:

Caudrey-Beals-Coifman system; conservation laws; soliton equation; Lax representation; Lie algebras