The Riemann-Hilbert problem and long-time asymptotics for the Kundu-Eckhaus equation with decaying initial value

DOI10.1016/j.aml.2017.08.006zbMath1383.35137OpenAlexW2746194579MaRDI QIDQ1680016

Jian Xu, Qiaozhen Zhu, En-gui Fan

Publication date: 22 November 2017

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.aml.2017.08.006

zbMATH Keywords

Riemann-Hilbert probleminitial value problemlong-time asymptoticDeift-Zhou nonlinear steepest descent methodKundu-Eckhaus equation

Mathematics Subject Classification ID

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

Related Items (21)

Long-time asymptotics for the Hirota equation on the half-line ⋮ Long-time asymptotics for the Kundu–Eckhaus equation on the half-line ⋮ Inelastic interactions, numerical breathers and chaotic wave fields for a focusing Kundu–Eckhaus equation in a nonlinear optical fiber ⋮ Long-time asymptotics for a mixed nonlinear Schrödinger equation with the Schwartz initial data ⋮ \(l^2\)-Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems ⋮ Rational soliton solutions in the nonlocal coupled complex modified Korteweg-de Vries equations ⋮ Numerical inverse scattering transform for the focusing and defocusing Kundu-Eckhaus equations ⋮ Exact multi-Soliton solutions of the KdV equation with a source: Riemann-Hilbert formulation ⋮ Breather, lump, and interaction solutions to a nonlocal KP system ⋮ Rogue wave and multi-pole solutions for the focusing Kundu-Eckhaus equation with nonzero background via Riemann-Hilbert problem method ⋮ The \(n\)-fold Darboux transformation for the Kundu-Eckhaus equation and dynamics of the smooth positon solutions ⋮ A \(\overline{\partial } \)-dressing method for the mixed Chen-Lee-Liu derivative nonlinear Schrödinger equation ⋮ Long time asymptotics behavior of the focusing nonlinear Kundu-Eckhaus equation ⋮ Dynamics of soliton solutions of the nonlocal Kundu-nonlinear Schrödinger equation ⋮ Long-time asymptotics of the focusing Kundu-Eckhaus equation with nonzero boundary conditions ⋮ A \(\overline{\partial}\)-dressing approach to the Kundu-Eckhaus equation ⋮ Dynamic behaviors of mixed localized solutions for the three-component coupled Fokas-Lenells system ⋮ Long-Time Asymptotics for the Nonlocal MKdV Equation* ⋮ Nonlocal-derivative NLS equations and group-invariant soliton solutions ⋮ A Riemann-Hilbert approach to the initial-boundary value problem for Kundu-Eckhaus equation on the half line ⋮ Explicit solutions to a nonlocal 2-component complex modified Korteweg-de Vries equation

Cites Work

• Unnamed Item
• Unnamed Item
• Long-time asymptotics for the Korteweg-de Vries equation via nonlinear steepest descent
• Long-time asymptotics for the Fokas-Lenells equation with decaying initial value problem: without solitons
• A Riemann-Hilbert approach to the initial-boundary problem for derivative nonlinear Schrödinger equation
• A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
• Two–dimensional linear partial differential equations in a convex polygon
• Long-time Asymptotics for the Camassa–Holm Equation
• The Kundu–Eckhaus equation and its discretizations
• Nonlinear evolution equations, rescalings, model PDES and their integrability: I
• 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
• Higher order asymptotics of the modified non-linear schrödinger equation
• On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method
• The Darboux transformation of the Kundu–Eckhaus equation

This page was built for publication: The Riemann-Hilbert problem and long-time asymptotics for the Kundu-Eckhaus equation with decaying initial value