Continuous Symmetries of the Lattice Potential KdV Equation

TL;DR

This paper investigates the integrability and symmetries of the lattice potential KdV equation, constructing soliton solutions and infinite symmetry sequences using spectral and Lax methods, including non-autonomous symmetries.

Contribution

It introduces a comprehensive analysis of the lpKdV equation's symmetries and solutions, including new non-autonomous generalized symmetries derived from discrete symmetries.

Findings

Constructed soliton solutions using spectral methods

Derived infinite sequences of generalized symmetries via Lax technique

Developed a class of non-autonomous symmetries from discrete symmetry

Abstract

In this paper we present a set of results on the integration and on the symmetries of the lattice potential Korteweg-de Vries (lpKdV) equation. Using its associated spectral problem we construct the soliton solutions and the Lax technique enables us to provide infinite sequences of generalized symmetries. Finally, using a discrete symmetry of the lpKdV equation, we construct a large class of non-autonomous generalized symmetries.