Solutions of the Ablowitz-Kaup-Newell-Segur hierarchy equations of the ``rogue wave type: a unified approach

DOI10.1134/S0040577916020033zbMath1342.35348OpenAlexW2320883575WikidataQ57936698 ScholiaQ57936698MaRDI QIDQ292808

Vladimir B. Matveev, Aleksandr Olegovich Smirnov

Publication date: 9 June 2016

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577916020033

zbMATH Keywords

nonlinear Schrödinger equationAKNS hierarchyrogue wavefreak waveHirota equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Shock waves and blast waves in fluid mechanics (76L05) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60)

Related Items (16)

ON THE COMPLEX MIXED DARK-BRIGHT WAVE DISTRIBUTIONS TO SOME CONFORMABLE NONLINEAR INTEGRABLE MODELS ⋮ New function solutions of Ablowitz-Kaup-Newell-Segur water wave equation via power index method ⋮ Elliptic solitons and “freak waves” ⋮ Characteristics of the breather and rogue waves in a (2+1)-dimensional nonlinear Schrödinger equation ⋮ A matrix Baker-Akhiezer function associated with the Maxwell-Bloch equations and their finite-gap solutions ⋮ The height of an \(n\)th-order fundamental rogue wave for the nonlinear Schrödinger equation ⋮ Cauchy problem for the nonlinear Hirota equation in the class of periodic infinite-zone functions ⋮ Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation ⋮ Cauchy problem for the nonlinear Liouville equation in the class of periodic infinite-gap functions ⋮ Integration of the modified Korteweg-de Vries-Liouville equation in the class of periodic infinite-gap functions ⋮ Rogue-wave solutions of the Zakharov equation ⋮ Multiphase solutions of nonlocal symmetric reductions of equations of the AKNS hierarchy: general analysis and simplest examples ⋮ Generalized invariant manifolds for integrable equations and their applications ⋮ Two-phase periodic solutions to the AKNS hierarchy equations ⋮ AKNS and NLS hierarchies, MRW solutions, P n breathers, and beyond ⋮ Dispersive shock wave, generalized Laguerre polynomials, and asymptotic solitons of the focusing nonlinear Schrödinger equation

Cites Work

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