The general mixed nonlinear Schrödinger equation: Darboux transformation, rogue wave solutions, and modulation instability
type: Item
instance of: scholarly article
title: The general mixed nonlinear Schrödinger equation: Darboux transformation, rogue wave solutions, and modulation instability
zbMATH Open document ID: 1419.37064
author: Y. Aharonov
published in: Advances in Difference Equations
publication date: 2018-12-03T00:00:00Z
Mathematics Subject Classification ID: 37K10
Mathematics Subject Classification ID: 35Q55
zbMATH DE Number: 6988079
zbMATH Keywords: Darboux transformation
zbMATH Keywords: rogue wave solution
zbMATH Keywords: general mixed nonlinear Schrödinger equation
zbMATH Keywords: Lax pair
zbMATH Keywords: modulation instability
MaRDI profile type: Publication
full work available at URL: s13662-016-0937-9
OpenAlex ID: W2510197905
Wikidata QID: Q59466498
cites work: Q3925229
cites work: Q4002235
cites work: Darboux transformation of the general Hirota equation: multisoliton solutions, breather solutions, and rogue wave solutions
cites work: Backlund transformations for the Nizhnik–Novikov–Veselov equation
cites work: Integrability and exact solutions of a two-component Korteweg-de Vries system
cites work: Integrability and equivalence relationships of six integrable coupled Korteweg-de Vries equations
cites work: Integrable properties of the general coupled nonlinear Schrödinger equations
cites work: Integrability and bright soliton solutions to the coupled nonlinear Schrödinger equation with higher-order effects
cites work: Prolongation structures and matter-wave solitons in \(F=1\) spinor Bose-Einstein condensate with time-dependent atomic scattering lengths in an expulsive harmonic potential
cites work: Exact Solution of the Korteweg—de Vries Equation for Multiple Collisions of Solitons
cites work: Double Wronskian solution and soliton properties of the nonisospectral BKP equation
cites work: Symmetry analysis and reductions of the two-dimensional generalized Benney system via geometric approach
cites work: Solitary wave solutions for a generalized Hirota-Satsuma coupled KdV equation by homotopy perturbation method
cites work: Further improved F-expansion method and new exact solutions of Konopelchenko--Dubrovsky equation
cites work: Dynamics and stability of stationary states for the spin-1 Bose-Einstein condensates in a standing light wave
cites work: Q4585381
cites work: On fractional Schrödinger equation in \(\alpha \)-dimensional fractional space
cites work: A fractional Schrödinger equation and its solution
cites work: Water waves, nonlinear Schrödinger equations and their solutions
cites work: On \(N\)th-order rogue wave solution to the generalized nonlinear Schrödinger equation
cites work: Generalized Darboux transformation and rogue wave solutions for the higher-order dispersive nonlinear Schrödinger equation
cites work: A generalization of inverse scattering method
cites work: Bäcklund transformations, soliton solutions and wave functions of Kaup–Newell and Wadati–Konno–Ichikawa systems
cites work: Homoclinic connections of unstable plane waves of the modified nonlinear Schrödinger equation
cites work: Darboux transformation and soliton-like solutions of nonlinear Schrödinger equations
cites work: Soliton and breather solutions of the modified nonlinear Schrödinger equation
cites work: Determinant representation of Darboux transformation for the AKNS system
cites work: Conservation laws, soliton solutions and modulational instability for the higher-order dispersive nonlinear Schrödinger equation
DOI: 10.1186/S13662-016-0937-9
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description: scientific article; zbMATH DE number 6988079