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

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, auxiliary equations of integrable models which means various cases of nonlinear Toda lattice equations and anomalous diffusion equation. (C) 2002 American Institute of Physics.