Discrete approximations on functional classes for the integrable\n nonlinear Schr "odinger dynamical system: a symplectic finite-dimensional\n reduction approach

2014/03/27 by Jan L. Cieśliński, Cieśliński, Jan L., Anatolij K. Prykarpatski +1
Mathematics · Physics and Astronomy · #35Q55 #37J15 #65P10 #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1403.7127

openalex publication_date 2014/03/27 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We investigate discretizations of the integrable discrete nonlinear\nSchr "odinger dynamical system and related symplectic structures. We develop an\neffective scheme of invariant reducing the corresponding infinite system of\nordinary differential equations to an equivalent finite system of ordinary\ndifferential equations with respect to the evolution parameter. We construct a\nfinite set of recurrent algebraic regular relations allowing to generate\nsolutions of the discrete nonlinear Schr "odinger dynamical system and we\ndiscuss the related functional spaces of solutions. Finally, we discuss the\nFourier transform approach to studying the solution set of the discrete\nnonlinear Schr "odinger dynamical system and its functional-analytical aspects.\n

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