Dispersion law degeneracy and multidimensional integrable differential equations

Abstract

Dispersion law classification for differential equations according to their degeneracy and integrability investigation of concrete systems of non-linear differential equations, considered in physics are the aim of the paper. It has been proved, that only two-dimensional dispersion laws may be degenerated while observing some sensible analytical conditions, and their explicit form has been obtained. Properties of some differential equations, considered in physics, have been investigated. In particular, integrability necessary and sufficient conditions for Zakharov-Mikhailov equation systems and non-symmetric field on SO(4) have been obtainedAvailable from VNTIC / VNTIC - Scientific & Technical Information Centre of RussiaSIGLERURussian Federatio