Two-fold integrable hierarchy of nonholonomic deformation of the DNLS and the Lenells-Fokas equation

Abstract

The concept of the nonholonomic deformation formulated recently for the AKNS family is extended to the Kaup-Newell class. Applying this construction we discover a novel two-fold integrable hierarchy related to the deformed derivative nonlinear Schrödinger (DNLS) equation and found the exact soliton solutions exhibiting unusual accelerating motion for both its field and the perturbing functions. Extending the idea of deformation the integrable perturbation of the gauge related Chen-Lee-Liu DNLS equation is constructed together with its soliton solution. We show that, the recently proposed Lenells-Fokas (LF) equation falls in the deformed DNLS hierarchy, sharing the accelerating soliton and other unusual features. Higher order integrable deformations of the LF and the DNLS equations are proposed.

16 pages, Latex, 3 figures

References in corpus (7)

• On a novel integrable generalization of the nonlinear Schrödinger equation
• 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
• Nonlinearizing linear equations to integrable systems including new hierarchies with nonholonomic deformations
• Dressing for a novel integrable generalization of the nonlinear Schrödinger equation

Cited by in corpus (7)

• A direct method of solution for the Fokas-Lenells derivative nonlinear Schrödinger equation: I. Bright soliton solutions
• Perturbation theory for solitons of the Fokas--Lenells equation : Inverse scattering transform approach
• Study of quasi-integrable and non-holonomic deformation of equations in the NLS and DNLS hierarchy
• Non-holonomic and Quasi-integrable deformations of the AB Equations
• Algebro-geometric solutions and their reductions for the Fokas-Lenells hierarchy
• 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