Integrability aspects and multi-soliton solutions of a new coupled Gerdjikov-Ivanov derivative nonlinear Schrödinger equation

DOI10.1007/s11071-019-04821-0zbMath1437.37083OpenAlexW2915077693MaRDI QIDQ783529

Jian-Ping Wu

Publication date: 4 August 2020

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-019-04821-0

zbMATH Keywords

inverse scattering transformspectral structuresoliton dynamicscoupled Gerdjikov-Ivanov equationintegrability aspects

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) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with algebraic geometry, complex analysis, and special functions (37K20) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15)

Related Items (14)

Localized waves for the coupled mixed derivative nonlinear Schrödinger equation in a birefringent optical fiber ⋮ Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data ⋮ Conservation laws, soliton solutions and modulation instability for the coupled Gerdjikov-Ivanov equations ⋮ Dynamic behaviors of vector breather waves and higher-order rogue waves in the coupled Gerdjikov-Ivanov equation ⋮ \(N\)-(soliton, breather) interactions for general multi-component third-fifth-order mKdV equations via Riemann-Hilbert method ⋮ Soliton, breather and rogue wave solutions of the coupled Gerdjikov-Ivanov equation via Darboux transformation ⋮ Bilinear Bäcklund transformation, Lax pair and interactions of nonlinear waves for a generalized \((2 + 1)\)-dimensional nonlinear wave equation in nonlinear optics/fluid mechanics/plasma physics ⋮ Quasi-Grammian solutions of the coupled Gerdjikov-Ivanov equation ⋮ Riemann-Hilbert method for multi-soliton solutions of a fifth-order nonlinear Schrödinger equation ⋮ Coupled derivative nonlinear Schrödinger III equation: Darboux transformation and higher-order rogue waves in a two-mode nonlinear fiber ⋮ Analysis and comparative study of non-holonomic and quasi-integrable deformations of the nonlinear Schrödinger equation ⋮ Riemann-Hilbert approach of the Newell-type long-wave-short-wave equation via the temporal-part spectral analysis ⋮ Bright and dark solitons and periodic wave solutions for the Gerdjikov-Ivanov equation in nonlinear fiber optics ⋮ Higher-order rogue waves solutions of the modified Gerdjikov-Ivanov equation with dispersion via generalized Darboux transformation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Envelope bright- and dark-soliton solutions for the Gerdjikov-Ivanov model
• Bifurcations and new exact travelling wave solutions for the Gerdjikov-Ivanov equation
• General \(N\)-solitons and their dynamics in several nonlocal nonlinear Schrödinger equations
• The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws
• The inverse scattering transform and soliton solutions of a combined modified Korteweg-de Vries equation
• Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system
• A Riemann-Hilbert approach for a new type coupled nonlinear Schrödinger equations
• Long-time asymptotics and the bright \(N\)-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach
• Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies
• Trace formula and new form of \(N\)-soliton to the Gerdjikov-Ivanov equation
• New integrable systems of derivative nonlinear Schrödinger equations with multiple components
• Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation
• Darboux transformations and global solutions for a nonlocal derivative nonlinear Schrödinger equation
• Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Derivative nonlinear Schrodinger equations and Hermitian symmetric spaces
• An exact solution for a derivative nonlinear Schrödinger equation
• Integrability of Nonlinear Hamiltonian Systems by Inverse Scattering Method
• Darboux transformation and soliton-like solutions for the Gerdjikov-Ivanov equation
• Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions
• N-Soliton Collision in the Manakov Model
• Soliton interactions in the vector NLS equation
• SOLUTIONS OF A DERIVATIVE NONLINEAR SCHRÖDINGER HIERARCHY AND ITS SIMILARITY REDUCTION

This page was built for publication: Integrability aspects and multi-soliton solutions of a new coupled Gerdjikov-Ivanov derivative nonlinear Schrödinger equation