A generalization of the Landau-Lifschitz equation: breathers and rogue waves

DOI10.1080/14029251.2020.1700636zbMath1436.37086OpenAlexW3004174762MaRDI QIDQ5212613

Ruomeng Li, Bo Xue, Xiangguo Geng

Publication date: 29 January 2020

Published in: Journal of Nonlinear Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14029251.2020.1700636

zbMATH Keywords

solitonsrogue wavesAkhmediev breathers\(N\)-fold generalized Darboux transformationgeneralized uniaxial Landau-Lifschitz equation

Mathematics Subject Classification ID

KdV equations (Korteweg-de Vries equations) (35Q53) Soliton equations (35Q51) Lie-Bäcklund and other transformations for infinite-dimensional Hamiltonian and Lagrangian systems (37K35)

Related Items (1)

Hodograph transformation, various exact solutions and dynamical analysis for the complex Wadati-Konno-Ichikawa-II equation

Cites Work

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• Initial-boundary problems for the vector modified Korteweg-de Vries equation via Fokas unified transform method
• Darboux transformation and exact multisolitons of \(\mathbb{C}P^N\) nonlinear sigma model
• Landau-Lifshitz equation, uniaxial anisotropy case: theory of exact solutions
• Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
• Darboux transformation of the Drinfeld-Sokolov-Satsuma-Hirota system and exact solutions
• The Riemann boundary problem on a torus and the inverse scattering problem for the Landau-Lifschitz equation
• The nonlinear dynamics of rogue waves and holes in deep-water gravity wave trains
• The Riemann boundary problem on Riemann surfaces and the inverse scattering problem for the Landau-Lifschitz equation
• Long-time asymptotics for integrable systems. Higher order theory
• Lump solutions to nonlinear partial differential equations via Hirota bilinear forms
• Long-time behavior of solutions to the derivative nonlinear Schrödinger equation for soliton-free initial data
• Rogue-wave solutions of the Zakharov equation
• 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
• Gauge equivalent structure and solitary wave solution for a modified Landau-Lifshitz equation
• Periodic and rational solutions of the reduced Maxwell-Bloch equations
• Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation
• Effective generation of closed-form soliton solutions of the continuous classical Heisenberg ferromagnet equation
• Darboux transformations in integrable systems. Theory and their applications to geometry
• Initial-Boundary Value Problem for Integrable Nonlinear Evolution Equation with 3 × 3 Lax Pairs on the Interval
• Darboux transformation for a two-component derivative nonlinear Schrödinger equation
• Long-Time Asymptotics for Solutions of the NLS Equation with a Delta Potential and Even Initial Data
• Discrete coupled derivative nonlinear Schrödinger equations and their quasi-periodic solutions
• An exact solution for a derivative nonlinear Schrödinger equation
• Darboux Transformation and Soliton Solutions for Generalized Nonlinear Schrödinger Equations
• The vector derivative nonlinear Schrödinger equation on the half-line
• Rogue periodic waves of the focusing nonlinear Schrödinger equation
• Rogue periodic waves of the modified KdV equation
• Rogue Waves for an Alternative System of Coupled Hirota Equations: Structural Robustness and Modulation Instabilities
• Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line
• An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line
• Binary Darboux transformation for the coupled Sasa-Satsuma equations
• The method of Darboux transformation matrix for solving the Landau-Lifschitz equation for a spin chain with an easy plane
• High‐Order Soliton Solution of Landau–Lifshitz Equation
• Hyperbolic methods for the Landau–Lifschitz inverse scattering problem
• Darboux and binary Darboux transformations for discrete integrable systems I. Discrete potential KdV equation

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