Inverse scattering transform and soliton classification of higher-order nonlinear Schrödinger-Maxwell-Bloch equations

DOI10.1134/S004057792006001XzbMath1445.81076MaRDI QIDQ2193736

Jin-Jie Yang, Shou-Fu Tian, Wei-Qi Peng, Zhi-Qiang Li

Publication date: 20 August 2020

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

soliton solutionbreatherRiemann-Hilbert methodhigher-order nonlinear Schrödinger-Maxwell-Bloch equation

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) PDEs in connection with optics and electromagnetic theory (35Q60) Quantum optics (81V80) NLS equations (nonlinear Schrödinger equations) (35Q55) Composite media; random media in optics and electromagnetic theory (78A48) Soliton solutions (35C08) Maxwell equations (35Q61)

Related Items (9)

The N-soliton solution to the higher-order nonlinear Schrödinger–Maxwell–Bloch system via the Riemann–Hilbert approach ⋮ A Riemann-Hilbert approach in the form of a block matrix for the coupled matrix integrable system ⋮ Inverse Scattering Transform and Soliton Solutions for the Hirota Equation with $N$ Distinct Arbitrary Order Poles ⋮ The general fifth-order nonlinear Schrödinger equation with nonzero boundary conditions: inverse scattering transform and multisoliton solutions ⋮ Riemann–Hilbert problem for the Fokas–Lenells equation in the presence of high-order discrete spectrum with non-vanishing boundary conditions ⋮ Inverse Scattering Method for Constructing Multisoliton Solutions of Higher-Order Nonlinear Schrödinger Equations ⋮ Inverse scattering transform and dynamics of soliton solutions for nonlocal focusing modified Korteweg-de Vries equation ⋮ Riemann-Hilbert problem for the modified Landau-Lifshitz equation with nonzero boundary conditions ⋮ Pure soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Breathers and localized solitons for the Hirota-Maxwell-Bloch system on constant backgrounds in erbium doped fibers
• Initial-boundary value problems for the general coupled nonlinear Schrödinger equation on the interval via the Fokas method
• Integrability and bright soliton solutions to the coupled nonlinear Schrödinger equation with higher-order effects
• Nonlinear Schrödinger equations and simple Lie algebras
• Integration of nonlinear equations of mathematical physics by the method of inverse scattering. II
• On the Riemann-Hilbert approach to asymptotic analysis of the correlation functions of the quantum nonlinear Schrödinger equation: Interacting fermion case
• Initial-boundary value problems for the coupled modified Korteweg-de Vries equation on the interval
• Riemann-Hilbert problems and \(N\)-soliton solutions for a coupled mKdV system
• Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation
• Integrability aspects of NLS-MB system with variable dispersion and nonlinear effects
• Inverse scattering transform and soliton classification of the coupled modified Korteweg-de Vries equation
• Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
• Riemann-Hilbert approach and \(N\)-soliton solutions for a generalized Sasa-Satsuma equation
• The Riemann-Hilbert problem for analytic description of the DM solitons
• The unified transform method for the Sasa–Satsuma equation on the half-line
• Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation
• Nonlinear Waves in Integrable and Nonintegrable Systems
• Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition
• Squared eigenfunctions for the Sasa–Satsuma equation
• Optical solitons in erbium-doped fibres with higher-order effects and pumping
• Initial-boundary value problems of the coupled modified Korteweg–de Vries equation on the half-line via the Fokas method
• An initial-boundary value problem for the integrable spin-1 Gross-Pitaevskii equations with a 4 × 4 Lax pair on the half-line
• Solitons in an erbium-doped nonlinear fibre medium with stimulated inelastic scattering
• General soliton matrices in the Riemann–Hilbert problem for integrable nonlinear equations
• The N‐coupled higher‐order nonlinear Schrödinger equation: Riemann‐Hilbert problem and multi‐soliton solutions
• Riemann-Hilbert method and N-soliton for two-component Gerdjikov-Ivanov equation
• Integrable properties of the general coupled nonlinear Schrödinger equations
• Inverse Scattering Transform of the Coupled Sasa–Satsuma Equation by Riemann–Hilbert Approach
• The mixed coupled nonlinear Schrödinger equation on the half-line via the Fokas method

This page was built for publication: Inverse scattering transform and soliton classification of higher-order nonlinear Schrödinger-Maxwell-Bloch equations