Lattice modified KdV hierarchy from a Lax pair expansion

TL;DR

This paper constructs a hierarchy of integrable lattice modified KdV equations through systematic Lax pair expansion, providing explicit solutions and recursion relations for each level.

Contribution

It introduces a method to generate and explicitly solve a hierarchy of integrable equations from a Lax pair expansion, advancing understanding of lattice modified KdV systems.

Findings

Hierarchy of integrable equations derived from Lax pair expansion

Explicit solutions for each equation in the hierarchy

Recursion relations connecting the equations

Abstract

We produce a hierarchiy of integrable equations by systematically adding terms to the Lax pair for the lattice modified KdV equation. The equations in the hierarchy are related to one aonother by recursion relations. These recursion relations are solved explicitly so that every equation in the hierarchy along with its Lax pair is known.