Planar unimodular Baker-Akhiezer function for the nonlinear Schrödinger equation

DOI10.4310/AMSA.2017.v2.n2.a6zbMath1386.35379OpenAlexW2742895194MaRDI QIDQ679643

Vladimir P. Kotlyarov, Dimitry Shepelsky

Publication date: 19 January 2018

Published in: Annals of Mathematical Sciences and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/amsa.2017.v2.n2.a6

zbMATH Keywords

Riemann-Hilbert problemsfinite-genus solutionsthe Baker-Akhiezer functionthe nonlinear Schrödinger equation

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Periodic solutions to PDEs (35B10) Almost and pseudo-almost periodic solutions to PDEs (35B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Boundary value problems in the complex plane (30E25)

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A matrix Baker-Akhiezer function associated with the Maxwell-Bloch equations and their finite-gap solutions ⋮ A Riemann-Hilbert method to algebro-geometric solutions of the Korteweg-de Vries equation ⋮ Phase computation for the finite-genus solutions to the focusing nonlinear Schrödinger equation using convolutional neural networks ⋮ Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method ⋮ Dispersive shock wave, generalized Laguerre polynomials, and asymptotic solitons of the focusing nonlinear Schrödinger equation

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