Symmetry-Preserving Difference Models of Some High-Order Nonlinear Integrable Equations

Abstract

In this paper, a procedure for constructing the symmetry-preserving difference models by means of the potential systems is employed to investigate some kinds of integrable equations. The invariant difference models for the Benjamin–Ono equation and the nonlinear dispersive $$K\left( {m,n} \right)$$ K m , n equation are investigated. Four cases of $$K\left( {m,n} \right)$$ K m , n equations which yield compactons are studied. The invariant difference models preserving all the symmetries are obtained. Furthermore, some linear combinations of the symmetries are used to construct the invariant difference models. The invariant difference model of the Hunter–Saxton equation is constructed. The idea of this paper can be further extended to discrete some other high-order nonlinear integrable equations.