Nonholonomic deformation of KdV and mKdV equations and their symmetries, hierarchies and integrability

TL;DR

This paper extends the concept of integrable nonholonomic deformation from the KdV equation to the mKdV and AKNS systems, revealing new hierarchies, soliton solutions, and symmetries that demonstrate their integrability.

Contribution

It introduces a novel nonholonomic deformation for the mKdV and AKNS systems, including a matrix Lax pair, new hierarchies, and exact soliton solutions with accelerating motion.

Findings

Deformed mKdV has a matrix Lax pair.

Existence of a two-fold integrable hierarchy.

Presence of infinitely many symmetries and conserved quantities.

Abstract

Recent concept of integrable nonholonomic deformation found for the KdV equation is extended to the mKdV equation and generalized to the AKNS system. For the deformed mKdV equation we find a matrix Lax pair, a novel two-fold integrable hierarchy and exact N-soliton solutions exhibiting unusual accelerating motion. We show that both the deformed KdV and mKdV systems possess infinitely many generalized symmetries, conserved quantities and a recursion operator.