Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations

TL;DR

This paper introduces a scheme to nonlinearize linear equations, generating new integrable systems and hierarchies with nonholonomic deformations, expanding the understanding of integrable models like KdV, mKdV, NLS, and SG.

Contribution

It presents a novel method for nonlinearizing linear equations to produce integrable systems, including new hierarchies with nonholonomic deformations across multiple classical equations.

Findings

Discovered a new integrable hierarchy with nonholonomic deformations.

Extended the universality of nonholonomic deformations to multiple equations.

Provided a systematic scheme based on dimensional analysis and Lax pair structure.

Abstract

We propose a scheme for nonlinearizing linear equations to generate integrable nonlinear systems of both the AKNS and the KN classes, based on the simple idea of dimensional analysis and detecting the building blocks of the Lax pair. Along with the well known equations we discover a novel integrable hierarchy of higher order nonholonomic deformations for the AKNS family, e.g. for the KdV, the mKdV, the NLS and the SG equation, showing thus a two-fold universality of the recently found deformation for the KdV equation.