A vector Geng-Li model: new nonlinear phenomena and breathers on periodic background waves

DOI10.1016/j.physd.2022.133270zbMath1490.35093OpenAlexW4220869105MaRDI QIDQ2140108

Ruomeng Li, Bo Xue, Xiangguo Geng

Publication date: 20 May 2022

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.physd.2022.133270

zbMATH Keywords

algebraic curvesDarboux transformationsrogue wavesBaker-Akhiezer functionsbreathers on periodic backgrounds

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) NLS equations (nonlinear Schrödinger equations) (35Q55) Soliton equations (35Q51) Soliton solutions (35C08)

Related Items (10)

Solitons, breathers and rogue waves in the coupled nonlocal reverse-time nonlinear Schrödinger equations ⋮ Dynamics of general higher-order rogue waves in the two-component long wave-short wave model of Newell type ⋮ Breather solutions to the AB system with non-zero background ⋮ Rogue-wave and breather solutions of the Fokas-Lenells equation on theta-function backgrounds ⋮ Localized wave solutions to the vector nonlinear Schrödinger equation with nonzero backgrounds ⋮ Higher-order mixed solution and breather solution on a periodic background for the Kundu equation ⋮ Rogue waves and breathers of the derivative Yajima-Oikawa long wave-short wave equations on theta-function backgrounds ⋮ Sasa-Satsuma type matrix integrable hierarchies and their Riemann-Hilbert problems and soliton solutions ⋮ Rogue waves on the periodic background in the complex modified KdV equation with higher-order effects ⋮ Rogue periodic waves of the short pulse equation and the coupled integrable dispersionless equation

Cites Work

• Unnamed Item
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• Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions
• Algebro-geometric constructions of the modified Boussinesq flows and quasi-periodic solutions
• Elastic and inelastic line-soliton solutions of the Kadomtsev-Petviashvili II equation
• Complex short pulse and coupled complex short pulse equations
• Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
• Integrable semi-discrete Kundu-Eckhaus equation: Darboux transformation, breather, rogue wave and continuous limit theory
• The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation
• Darboux transformation for an integrable generalization of the nonlinear Schrödinger equation
• Modulational instability of periodic standing waves in the derivative NLS equation
• A vector general nonlinear Schrödinger equation with \((m+n)\) components
• Rogue periodic waves of the sine-Gordon equation
• Rational solutions for a (3+1)-dimensional nonlinear evolution equation
• Intricate dynamics of rogue waves governed by the Sasa-Satsuma equation
• The Hirota equation: Darboux transform of the Riemann-Hilbert problem and higher-order rogue waves
• Periodic travelling waves of the modified KdV equation and rogue waves on the periodic background
• Baseband modulation instability, rogue waves and state transitions in a deformed Fokas-Lenells equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy
• Darboux transformations in integrable systems. Theory and their applications to geometry
• Long-time asymptotics for the spin-1 Gross-Pitaevskii equation
• The Application of Neumann Type Systems for Solving Integrable Nonlinear Evolution Equations
• Darboux transformation and multi-dark soliton forN-component nonlinear Schrödinger equations
• Darboux Transformation and Soliton Solutions for Generalized Nonlinear Schrödinger Equations
• Dynamics of lumps and dark–dark solitons in the multi-component long-wave–short-wave resonance interaction system
• Rogue periodic waves of the focusing nonlinear Schrödinger equation
• The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices
• Rogue periodic waves of the modified KdV equation
• Rogue waves of the nonlocal Davey–Stewartson I equation
• Multi‐breather and high‐order rogue waves for the nonlinear Schrödinger equation on the elliptic function background
• On a vector long wave‐short wave‐type model
• The general coupled Hirota equations: modulational instability and higher-order vector rogue wave and multi-dark soliton structures
• A long waves-short waves model: Darboux transformation and soliton solutions
• The Darboux transformation of the Kundu–Eckhaus equation
• Integrability properties of the differential-difference Kadomtsev–Petviashvili hierarchy and continuum limits

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