Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation

DOI10.1016/j.amc.2020.125469zbMath1497.35436OpenAlexW3040477263MaRDI QIDQ2656681

Bang-Qing Li, Yu-Lan Ma

Publication date: 16 March 2021

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125469

zbMATH Keywords

nonlinear Schrödinger systemrogue wavebreatherextended generalized Darboux transformationhybrid wave solution

Mathematics Subject Classification ID

NLS equations (nonlinear Schrödinger equations) (35Q55) Geometric theory, characteristics, transformations in context of PDEs (35A30)

Related Items (27)

Darboux transformation, soliton solutions of the variable coefficient nonlocal modified Korteweg-de Vries equation ⋮ Darboux transformation and exact solutions of the variable coefficient nonlocal Newell-Whitehead equation ⋮ Multiple breathers and rational solutions to Ito integro-differential equation arising in shallow water waves ⋮ Hybrid breather and rogue wave solution for a (2 + 1)-dimensional ferromagnetic spin chain system with variable coefficients ⋮ New fractal soliton solutions and sensitivity visualization for double-chain DNA model ⋮ A new (3+1)-dimensional Kadomtsev-Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves ⋮ Interactional solutions of the extended nonlinear Schrödinger equation with higher-order operators ⋮ APPRAISAL OF ANALYTICAL SOLUTIONS FOR (2 + 1)-DIMENSIONAL NONLINEAR CHIRAL SCHRÖDINGER EQUATION ⋮ Interaction properties between rogue wave and breathers to the Manakov system arising from stationary self-focusing electromagnetic systems ⋮ Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity ⋮ Mixed higher-order rogue waves and solitons for the coupled modified nonlinear Schrödinger equation ⋮ Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation ⋮ Interaction behaviors between solitons, breathers and their hybrid forms for a short pulse equation ⋮ Hybrid rogue wave and breather solutions for the nonlinear coupled dispersionless evolution equations ⋮ Nonlocal Yajima-Oikawa system: binary Darboux transformation, exact solutions and dynamic properties ⋮ Binary Darboux transformation, solitons, periodic waves and modulation instability for a nonlocal Lakshmanan-Porsezian-Daniel equation ⋮ Higher-order mixed solution and breather solution on a periodic background for the Kundu equation ⋮ Rogue waves of the sixth-order nonlinear Schrödinger equation on a periodic background ⋮ Hybrid soliton and breather waves, solution molecules and breather molecules of a \((3+1)\)-dimensional Geng equation in shallow water waves ⋮ The abundant mixed solutions of \((2+1)\)-dimensional potential Yu-Toda-Sasa-Fukuyama equation ⋮ Loop-like kink breather and its transition phenomena for the Vakhnenko equation arising from high-frequency wave propagation in electromagnetic physics ⋮ Mixed localized wave solutions of the Hirota equation ⋮ Solitons and dynamics for the integrable nonlocal pair-transition-coupled nonlinear Schrödinger equation ⋮ Mixed rational lump-solitary wave solutions to an extended (2+1)-dimensional KdV equation ⋮ Application of the multiple exp-function, cross-kink, periodic-kink, solitary wave methods, and stability analysis for the CDG equation ⋮ Integrability aspects and some abundant solutions for a new (4 + 1)-dimensional KdV-like equation ⋮ A complex short pulse system in optical-fiber communications: rogue waves and phase transitions

Cites Work

• New rogue waves and dark-bright soliton solutions for a coupled nonlinear Schrödinger equation with variable coefficients
• Conservation laws, bilinear forms and solitons for a fifth-order nonlinear Schrödinger equation for the attosecond pulses in an optical fiber
• Envelope bright- and dark-soliton solutions for the Gerdjikov-Ivanov model
• Rogue waves, homoclinic breather waves and soliton waves for the \((2 + 1)\)-dimensional B-type Kadomtsev-Petviashvili equation
• Waves that appear from nowhere and disappear without a trace
• A soliton hierarchy associated with \(\mathrm{so}(3,\mathbb R)\)
• Exact first-order solutions of the nonlinear Schrödinger equation
• The rogue waves of the KP equation with self-consistent sources
• The \(N\)-loop soliton solutions for \((2+1)\)-dimensional Vakhnenko equation
• On the solitary waves, breather waves and rogue waves to a generalized \((3+1)\)-dimensional Kadomtsev-Petviashvili equation
• Higher-order integrable evolution equation and its soliton solutions
• Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation
• Multiple-lump waves for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation arising from incompressible fluid
• Darboux transformation and classification of solution for mixed coupled nonlinear Schrödinger equations
• Lax pair, Darboux transformation and \(N\)th-order rogue wave solutions for a (2+1)-dimensional Heisenberg ferromagnetic spin chain equation
• Rogue waves, rational solutions, the patterns of their zeros and integral relations
• A series of the solutions for the Heisenberg ferromagnetic spin chain equation
• Analytic rogue wave solutions for a generalized fourth‐order Boussinesq equation in fluid mechanics
• General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation

This page was built for publication: Extended generalized Darboux transformation to hybrid rogue wave and breather solutions for a nonlinear Schrödinger equation