New interaction solutions from Lax pair related symmetry of the Generalized fifth order KdV equation

TL;DR

This paper derives new interaction solutions for the generalized fifth order KdV equation by exploiting nonlocal symmetries from its Lax pair, localizing them, and applying symmetry reduction techniques.

Contribution

It introduces a novel method to obtain interaction solutions for the FOKdV equation using nonlocal symmetries derived from the Lax pair.

Findings

New interaction solutions for the FOKdV equation

A method to localize nonlocal symmetries via an enlarged system

Derivation of a new Bäcklund transformation

Abstract

The nonlocal symmetry of the generalized fifth order KdV equation (FOKdV) is first obtained by using the related Lax pair and then localized in a new enlarged system by introducing some new variables. On this basis, new Backlund transformation is obtained through Lie's first theorem. Furthermore, the general form of Lie point symmetry for the enlarged FOKdV system is found and new interaction solutions for the FOKdV equation are explored by using classical symmetry reduction method.