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

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.

17 pages, 5 figures, Latex, Final version to be published in J. Math. Phys

References in corpus (5)

• Dynamics of semifluxons in Nb long Josephson 0-pi junctions
• KdV6: An Integrable System
• A new integrable generalization of the Korteweg - de Vries equation
• Nonholonomic deformation of KdV and mKdV equations and their symmetries, hierarchies and integrability
• Exact accelerating solitons in nonholonomic deformation of the KdV equation with two-fold integrable hierarchy

Cited by in corpus (4)

• Two-fold integrable hierarchy of nonholonomic deformation of the DNLS and the Lenells-Fokas equation
• 2+1 KdV(N) Equations
• On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources
• Analysis and comparative study of non-holonomic and quasi-integrable deformations of the Nonlinear Schrödinger Equation