Integrable discretizations of derivative nonlinear Schr dinger equations
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Publication:4467975
DOI10.1088/0305-4470/35/36/310zbMATH Open1040.37061arXivnlin/0105053OpenAlexW2022368383MaRDI QIDQ4467975
Author name not available (Why is that?)
Publication date: 10 June 2004
Published in: (Search for Journal in Brave)
Abstract: We propose integrable discretizations of derivative nonlinear Schroedinger (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 Schroedinger (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.
Full work available at URL: https://arxiv.org/abs/nlin/0105053
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