Long-time asymptotics for the modified complex short pulse equation

DOI10.3934/dcds.2022060zbMath1494.35032OpenAlexW4226358984MaRDI QIDQ2158220

Kedong Wang, Mingming Chen, Xiangguo Geng

Publication date: 26 July 2022

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcds.2022060

zbMATH Keywords

Riemann-Hilbert problemspectral analysislong-time asymptoticsinverse scattering methodnonlinear steepest descent methodmodified complex short pulse equation

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Soliton equations (35Q51) Riemann-Hilbert problems in context of PDEs (35Q15)

Related Items

The Riemann-Hilbert approach for the higher-order Gerdjikov-Ivanov equation, soliton interactions and position shift ⋮ Inverse scattering transform for the coupled modified complex short pulse equation: Riemann-Hilbert approach and soliton solutions ⋮ Long-time asymptotics for the coupled complex short-pulse equation with decaying initial data ⋮ Soliton resolution for the complex short-pulse positive flow with weighted Sobolev initial data in the space-time soliton regions ⋮ Spectral analysis and long-time asymptotics for the Harry Dym-type equation with the Schwartz initial data

Cites Work

• Unnamed Item
• Unnamed Item
• Long-time asymptotics for solutions of the NLS equation with a delta potential and even initial data: announcement of results
• Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent
• Riemann-Hilbert approach for the Camassa-Holm equation on the line
• Long-time asymptotics for the focusing NLS equation with time-periodic boundary condition on the half-line
• Long-time asymptotics for the short pulse equation
• The nonlinear steepest descent method to long-time asymptotics of the coupled nonlinear Schrödinger equation
• The Deift-Zhou steepest descent method to long-time asymptotics for the Sasa-Satsuma equation
• Propagation of ultra-short optical pulses in cubic nonlinear media
• The application of the theory of trigonal curves to the discrete coupled nonlinear Schrödinger hierarchy
• Spectral analysis and long-time asymptotics for the potential Wadati-Konno-Ichikawa equation
• A vector general nonlinear Schrödinger equation with \((m+n)\) components
• Rogue periodic waves of the sine-Gordon equation
• Long-time asymptotic behavior for the complex short pulse equation
• The bi-Hamiltonian structure of the short pulse equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• The short pulse equation by a Riemann-Hilbert approach
• Riemann-Hilbert approach and \(N\)-soliton solutions for a generalized Sasa-Satsuma equation
• Long-time asymptotics for the Degasperis-Procesi equation on the half-line
• Long-time asymptotics of the coupled modified Korteweg-de Vries equation
• The Ostrovsky-Vakhnenko equation: A Riemann-Hilbert approach
• Algebro-geometric solutions of the coupled modified Korteweg-de Vries hierarchy
• Long-time asymptotics for the spin-1 Gross-Pitaevskii equation
• Integrable multi-component generalization of a modified short pulse equation
• Riemann-Hilbert approach and N-soliton formula for coupled derivative Schrödinger equation
• Ultra-short pulses in linear and nonlinear media
• The short-wave model for the Camassa–Holm equation: a Riemann–Hilbert approach
• The short pulse hierarchy
• On Equations Which Describe Pseudospherical Surfaces
• Long-time Asymptotics for the Camassa–Holm Equation
• Scattering and inverse scattering for first order systems
• Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Nonvanishing Continuous Background
• Long-time asymptotics for the pure radiation solution of the sine—gordon equation
• Leading-order temporal asymptotics of the modified nonlinear Schrödinger equation: solitonless sector
• Higher order asymptotics of the modified non-linear schrödinger equation
• The Riemann theta function solutions for the hierarchy of Bogoyavlensky lattices
• Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line
• General soliton matrices in the Riemann–Hilbert problem for integrable nonlinear equations
• On a vector long wave‐short wave‐type model
• The Ostrovsky–Vakhnenko equation by a Riemann–Hilbert approach
• A modified complex short pulse equation of defocusing type
• Solitary wave solutions of the short pulse equation