Exotic localized vector waves in a two-component nonlinear wave system

DOI10.1007/s00332-019-09581-0zbMath1440.37068OpenAlexW2973119209WikidataQ127236117 ScholiaQ127236117MaRDI QIDQ2173677

Yao-Lin Jiang, Xiao-Yong Wen, Deng-Shan Wang, Ling Xu

Publication date: 17 April 2020

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00332-019-09581-0

zbMATH Keywords

Darboux transformationmodulational instabilityrogue waveslocalized vector waves

Mathematics Subject Classification ID

Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) (37K10) Stability problems for infinite-dimensional Hamiltonian and Lagrangian systems (37K45) Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems (37K40) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35) Traveling wave solutions (35C07)

Related Items (17)

Vector breather waves and higher-order rouge waves to the coupled higher-order nonlinear Schrödinger equations ⋮ \(N\)-fold Darboux transformation and soliton solutions for the relativistic Toda lattice equation ⋮ Variety interaction solutions comprising lump solitons for the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation ⋮ Transition of the breather wave of six-order nonlinear Schrödinger equation ⋮ Interactions of localized wave and dynamics analysis in generalized derivative nonlinear Schrödinger equation ⋮ A generalized complex mKdV equation: Darboux transformations and explicit solutions ⋮ Degenerate lump interactions within the Kadomtsev-Petviashvili equation ⋮ Modulation instability analysis of Rossby waves based on (2 + 1)-dimensional high-order Schrödinger equation ⋮ Negative order mKdV equation and \(N\)-solitons ⋮ Spectral stability of elliptic solutions to the short-pulse equation ⋮ M-lump solutions to the \((2+1)\)-dimensional generalized Calogero-Bogoyavlenshii-Schiff equation ⋮ Hybrid rogue wave and breather solutions for the nonlinear coupled dispersionless evolution equations ⋮ Exact multi-Soliton solutions of the KdV equation with a source: Riemann-Hilbert formulation ⋮ \(N\)-fold Darboux transformation and exact solutions for the nonlocal Fokas-Lenells equation on the vanishing and plane wave backgrounds ⋮ A generalized integrable lattice hierarchy associated with the Toda and modified Toda lattice equations: Hamiltonian representation, soliton solutions ⋮ Wave propagation of resonance multi-stripes, complexitons, and lump and its variety interaction solutions to the (2+1)-dimensional pKP equation ⋮ Nonlinear wave transitions and their mechanisms of (2+1)-dimensional Sawada-Kotera equation

Cites Work

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• A Bargmann system and the involutive solutions associated with a new 4-order lattice hierarchy
• A deformed reduced semi-discrete Kaup-Newell equation, the related integrable family and Darboux transformation
• Modulation instability: The beginning
• Bäcklund transformations and their applications
• Mixed lump-kink solutions to the KP equation
• Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
• Conservation laws by symmetries and adjoint symmetries
• Integrable semi-discrete Kundu-Eckhaus equation: Darboux transformation, breather, rogue wave and continuous limit theory
• Mixed lump-kink solutions to the BKP equation
• Lump solutions to a \((2+1)\)-dimensional extended KP equation
• Long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions
• Lump solutions to a generalized Bogoyavlensky-Konopelchenko equation
• Abundant lumps and their interaction solutions of \((3+1)\)-dimensional linear PDEs
• Integrability aspects of some two-component KdV systems
• A new nonlinear wave equation: Darboux transformation and soliton solutions
• Modulational instability and higher order-rogue wave solutions for the generalized discrete Hirota equation
• Inverse scattering transformation for generalized nonlinear Schrödinger equation
• Diversity of interaction solutions to the \((2+1)\)-dimensional ito equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• A new integrable symplectic map by the binary nonlinearization to the super AKNS system
• An integrable generalization of the D-Kaup-Newell soliton hierarchy and its bi-Hamiltonian reduced hierarchy
• Two integrable lattice hierarchies and their respective Darboux transformations
• A new integrable symplectic map and the lie point symmetry associated with nonlinear lattice equations
• Darboux Transformations and New Explicit Solutions for a Blaszak—Marciniak Three-Field Lattice Equation
• Binary Bargmann symmetry constraint associated with 3×3 discrete matrix spectral problem
• An integrable generalization of the nonlinear Schrödinger equation on the half-line and solitons
• A unified transform method for solving linear and certain nonlinear PDEs
• Higher-Order Rogue Wave and Rational Soliton Solutions of Discrete Complex mKdV Equations
• Moving breathers and breather-to-soliton conversions for the Hirota equation
• Generalised (2+1)-dimensional Super MKdV Hierarchy for Integrable Systems in Soliton Theory

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