Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy

TL;DR

This paper presents exact soliton solutions for a nonholonomically deformed KdV equation, revealing an accelerated motion and a novel two-fold integrable hierarchy with distinct dispersive properties.

Contribution

It introduces a new nonholonomic deformation of the KdV equation, constructs explicit N-soliton solutions, and uncovers a two-fold integrable hierarchy with unique features.

Findings

Exact N-soliton solutions with accelerated motion

Revelation of a two-fold integrable hierarchy

Identification of novel higher nonholonomic deformations

Abstract

Recently proposed nonholonomic deformation of the KdV equation is solved through inverse scattering method by constructing AKNS-type Lax pair. Exact and explicit N-soliton solutions are found for the basic field and the deforming function showing an unusual accelerated (decelerated) motion. A two-fold integrable hierarchy is revealed, one with usual higher order dispersion and the other with novel higher nonholonomic deformations.