Conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces

TL;DR

This paper derives conservation laws for nonlinear equations with variable coefficients on discrete and noncommutative spaces, providing explicit conserved charges and applying the method to quantum, supersymmetric, and integrable models.

Contribution

It introduces a general method to derive conservation laws for complex nonlinear equations on discrete and noncommutative spaces, including explicit conserved charges.

Findings

Conservation laws are derived for various nonlinear equations.

Explicit conserved charges are constructed for discrete models.

Applications include quantum plane, supersymmetric, and integrable models.

Abstract

The conservation laws for a class of nonlinear equations with variable coefficients on discrete and noncommutative spaces are derived. For discrete models the conserved charges are constructed explicitly. The applications of the general method include equations on quantum plane, supersymmetric equations for chiral and antichiral supermultiplets as well as auxiliary equations of integrable models - principal chiral model and various cases of nonlinear Toda lattice equations.