Integrable discretizations of derivative nonlinear Schr dinger equations

2001/05/31 by Takayuki Tsuchida · 2 citations
Mathematics · Physics and Astronomy · #Advanced Fiber Laser Technologies #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-th #math-ph #math.AP #math.MP #nlin.SI

paper · pdf · doi:10.1088/0305-4470/35/36/310

published as J.Phys.A35:7827,2002 · 24 pages, LaTeX2e (IOP style), final version

openalex publication_date 2002/08/27 · arxiv created 2002/08/28 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

Abstract

We propose integrable discretizations of derivative nonlinear Schrödinger (DNLS) equations such as the Kaup–Newell equation, the Chen–Lee–Liu equation and the Gerdjikov–Ivanov equation by constructing Lax pairs. The discrete DNLS systems admit the reduction of complex conjugation between two dependent variables and possess bi-Hamiltonian structure. Through transformations of variables and reductions, we obtain novel integrable discretizations of the nonlinear Schrödinger (NLS), modified KdV (mKdV), mixed NLS, matrix NLS, matrix KdV, matrix mKdV, coupled NLS, coupled Hirota, coupled Sasa–Satsuma and Burgers equations. We also discuss integrable discretizations of the sine-Gordon equation, the massive Thirring model and their generalizations.

Citations

• New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation
• Complete integrability of derivative nonlinear Schrödinger-type equations
• On the complete integrability of the two-dimensional classical Thirring model
• Symmetrically coupled higher-order nonlinear Schrödinger equations: singularity analysis and integrability
• Integrable semi-discretization of the coupled nonlinear Schrödinger equations

Cited by

• From AKNS to derivative NLS hierarchies via deformations of associative products
• Systematic method of generating new integrable systems via inverse Miura maps