Integrable Hierarchy of Higher Nonlinear Schrödinger Type Equations

Abstract

Addition of higher nonlinear terms to the well known integrable nonlinear Schrödinger (NLS) equations, keeping the same linear dispersion (LD) usually makes the system nonintegrable. We present a systematic method through a novel Eckhaus-Kundu hierarchy, which can generate higher nonlinearities in the NLS and derivative NLS equations preserving their integrability. Moreover, similar nonlinear integrable extensions can be made again in a hierarchical way for each of the equations in the known integrable NLS and derivative NLS hierarchies with higher order LD, without changing their LD.

arXiv commentPublished in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (2)

• Bilinearization of a Generalized Derivative Nonlinear Schrödinger equation
• The Painlevé methods

Cited by in corpus (4)

• Inverse scattering transform of an extended nonlinear Schrödinger equation with nonzero boundary conditions and its multisoliton solutions
• On Rogue wave in the Kundu-DNLS equation
• The rational solutions of the mixed nonlinear Schrödinger equation
• Inverse scattering transform for the Kundu-Eckhaus Equation with nonzero boundary condition