Maximal amplitudes of finite-gap solutions for the focusing nonlinear Schrödinger equation

DOI10.1007/s00220-017-2895-9zbMath1391.35348arXiv1601.00875OpenAlexW2962788742MaRDI QIDQ2406833

Alexander Tovbis, Marco Bertola

Publication date: 6 October 2017

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1601.00875

zbMATH Keywords

theta functioninverse scatteringNLS

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Theta functions and abelian varieties (14K25)

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Imaginary eigenvalues of Zakharov-Shabat problems with non-zero background, Rogue periodic waves of the focusing nonlinear Schrödinger equation, Rogue periodic waves of the modified KdV equation, A matrix Baker-Akhiezer function associated with the Maxwell-Bloch equations and their finite-gap solutions, Rogue periodic waves in the fifth-order Ito equation, A Riemann-Hilbert method to algebro-geometric solutions of the Korteweg-de Vries equation, Bounded ultra-elliptic solutions of the defocusing nonlinear Schrödinger equation, Finite gap integration of the derivative nonlinear Schrödinger equation: a Riemann-Hilbert method, On asymptotic regimes of orthogonal polynomials with complex varying quartic exponential weight, Sharp upper bound for amplitudes of hyperelliptic solutions of the focusing nonlinear Schrödinger equation, Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background, Periodic standing waves in the focusing nonlinear Schrödinger equation: rogue waves and modulation instability

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