Symmetries and conservation laws for a two-component discrete potentiated Korteweg - de Vries equation

Abstract

In the work we discuss briefly a method for constructing a formal asymptotic solution to a system of linear difference equations in the vicinity of a special value of the parameter. In the case when the system is the Lax pair for some nonlinear equation on a square graph, the found formal asymptotic solution allows us to describe the conservation laws and higher symmetries for this nonlinear equation. In the work we give a complete description of a series of conservation laws and the higher symmetries hierarchy for a discrete potential two-component Korteweg-de Vries equation.

Two‐level linearized and local uncoupled difference schemes for the two‐component evolutionary Korteweg‐de Vries system

“…Furthermore, some conservation laws were investigated based on the obtained Lax pair and the exact solutions for the two‐component KdV system were derived explicitly. In , a complete description of a series of conservation laws and the higher symmetries hierarchy for a discrete potential two‐component KdV equations were given when the system was the Lax pair for some nonlinear equation on a square graph.…”