Inverse scattering transform for the defocusing-defocusing coupled Hirota equations with non-zero boundary conditions: multiple double-pole solutions

DOI10.1016/j.physd.2024.134434MaRDI QIDQ6669499

Yi Zhang, Pengfei Han, Rusuo Ye, Ma Wen-Xiu

Publication date: 22 January 2025

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

zbMATH Keywords

inverse scattering transformRiemann-Hilbert problemnon-zero boundary conditionsgeneral coupled Hirota equationsmultiple double-pole solutions

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Scattering theory for PDEs (35P25) Asymptotic distributions of eigenvalues in context of PDEs (35P20) NLS equations (nonlinear Schrödinger equations) (35Q55) Lasers, masers, optical bistability, nonlinear optics (78A60) Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems (37K15) Riemann-Hilbert problems in context of PDEs (35Q15) Second-order parabolic equations (35K10) Soliton solutions (35C08) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

• Integrability and bright soliton solutions to the coupled nonlinear Schrödinger equation with higher-order effects
• Long-time asymptotics for the initial-boundary value problem of coupled Hirota equation on the half-line
• Generalized Darboux transformation and localized waves in coupled Hirota equations
• Application of the Riemann-Hilbert approach to the multicomponent AKNS integrable hierarchies
• Elastic and inelastic collisions of the semirational solutions for the coupled Hirota equations in a birefringent fiber
• Inverse scattering transform for the defocusing nonlinear Schrödinger equation with fully asymmetric non-zero boundary conditions
• The Riemann-Hilbert approach for the focusing Hirota equation with single and double poles
• Far-field asymptotics for multiple-pole solitons in the large-order limit
• Inverse scattering transform for the coupled modified Korteweg-de Vries equation with nonzero boundary conditions
• Asymptotic analysis of high-order solitons for the Hirota equation
• Focusing and defocusing Hirota equations with non-zero boundary conditions: inverse scattering transforms and soliton solutions
• Localized waves for the mixed coupled Hirota equations in an optical fiber
• Riemann-Hilbert method for the Wadati-Konno-Ichikawa equation: \(N\) simple poles and one higher-order pole
• Analytical solutions for the coupled Hirota equations in the firebringent fiber
• The Hirota equation: Darboux transform of the Riemann-Hilbert problem and higher-order rogue waves
• Large-order asymptotics for multiple-pole solitons of the focusing nonlinear Schrödinger equation
• Long-time asymptotics for the focusing nonlinear Schrödinger equation with nonzero boundary conditions in the presence of a discrete spectrum
• Sasa-Satsuma type matrix integrable hierarchies and their Riemann-Hilbert problems and soliton solutions
• The Inverse Scattering Transform for the Defocusing Nonlinear Schrödinger Equations with Nonzero Boundary Conditions
• Universal Nature of the Nonlinear Stage of Modulational Instability
• The focusing Manakov system with nonzero boundary conditions
• Direct and inverse scattering transforms with arbitrary spectral singularities
• Inverse scattering transform for the vector nonlinear Schrödinger equation with nonvanishing boundary conditions
• Inverse scattering method for square matrix nonlinear Schrödinger equation under nonvanishing boundary conditions
• Scattering and inverse scattering for first order systems
• Nonlinear Dynamics of Deep-Water Gravity Waves
• Scattering and inverse scattering for first-order systems: II
• Inverse scattering on the line
• The Inverse Scattering Transform‐Fourier Analysis for Nonlinear Problems
• Linear and Nonlinear Inverse Scattering
• Method for Solving the Korteweg-deVries Equation
• BILINEAR ESTIMATES AND APPLICATIONS TO NONLINEAR WAVE EQUATIONS
• Rogue Waves for an Alternative System of Coupled Hirota Equations: Structural Robustness and Modulation Instabilities
• The Riemann–Hilbert Problem and Inverse Scattering
• General soliton solutions to a reverse‐time nonlocal nonlinear Schrödinger equation
• Inverse scattering transforms and soliton solutions of nonlocal reverse‐space nonlinear Schrödinger hierarchies
• The regularity of the multiple higher‐order poles solitons of the NLS equation
• The general coupled Hirota equations: modulational instability and higher-order vector rogue wave and multi-dark soliton structures
• A Robust Inverse Scattering Transform for the Focusing Nonlinear Schrödinger Equation
• Inverse Scattering Transform for the Defocusing Manakov System with Nonzero Boundary Conditions
• Numerical inverse scattering for the focusing and defocusing nonlinear Schrödinger equations
• Inverse scattering transform for the focusing nonlinear Schrödinger equation with nonzero boundary conditions
• Integrals of nonlinear equations of evolution and solitary waves
• Inverse scattering transform for the integrable discrete nonlinear Schrödinger equation with nonvanishing boundary conditions
• Inverse Scattering Transform for the Defocusing Manakov System with Non-Parallel Boundary Conditions at Infinity
• Dark soliton solutions of the coupled Hirota equation in nonlinear fiber
• Inverse scattering transform for the two‐component Gerdjikov–Ivanov equation with nonzero boundary conditions: Dark‐dark solitons
• Large and infinite-order solitons of the coupled nonlinear Schrödinger equation
• Type \((\lambda^\ast,\lambda)\) reduced nonlocal integrable AKNS equations and their soliton solutions
• A four-component hierarchy of combined integrable equations with bi-Hamiltonian formulations

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