Integrable discretizations of derivative nonlinear Schrödinger equations
نویسنده
چکیده
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. Integrable discretizations of derivative nonlinear Schrödinger equations 2
منابع مشابه
Complete integrability of derivative nonlinear Schrödinger-type equations
We study matrix generalizations of derivative nonlinear Schrödinger-type equations, which were shown by Olver and Sokolov to possess a higher symmetry. We prove that two of them are ‘C-integrable’ and the rest of them are ‘S-integrable’ in Calogero’s terminology. PACS numbers: 02.10Jf, 02.30.Jr, 03.65.Ge, 11.30.-j Submitted to: Inverse Problems † E-mail address: [email protected]...
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