Leading Order Temporal Asymptotics of the Modified Non-Linear Schrodinger Equation: Solitonless Sector

Abstract

Using the matrix Riemann-Hilbert factorisation approach for non-linear evolution equations (NLEEs) integrable in the sense of the inverse scattering method, we obtain, in the solitonless sector, the leading-order asymptotics as $t$ tends to plus and minus infinity of the solution to the Cauchy initial-value problem for the modified non-linear Schrodinger equation: also obtained are analogous results for two gauge-equivalent NLEEs; in particular, the derivative non-linear Schrodinger equation.

29 pages, 5 figures, LaTeX, revised version of the original submission, to be published in Inverse Problems

Cited by in corpus (20)

• Soliton Resolution for the Derivative Nonlinear Schrödinger Equation
• Long-time asymptotic for the derivative nonlinear Schrödinger equation with decaying initial value
• Perturbation theory for the modified nonlinear Schr{ö}dinger solitons
• The Semiclassical Modified Nonlinear Schroedinger Equation I: Modulation Theory and Spectral Analysis
• Global Existence for the Derivative Nonlinear Schrodinger Equation by the Method of Inverse Scattering
• Existence of global solutions to the derivative NLS equation with the inverse scattering transform method
• Global Well-posedness and soliton resolution for the Derivative Nonlinear Schrödinger equation
• Riemann-Hilbert approach to the modified nonlinear Schröinger equation with non-vanishing asymptotic boundary conditions
• Long-Time Behavior of Solutions to the Derivative Nonlinear Schrödinger Equation for Soliton-Free Initial Data
• The long-time asymptotic of the derivative nonlinear Schr$\ddot{o}$dinger equation with step-like initial value
• Long-time asymptotic behavior of the modified Schrödinger equation via Dbar-steepest descent method
• Leading-order temporal asymptotics of the Fokas-Lenells Equation without solitons
• Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line
• Global Well-Posesedness for the Derivative Nonlinear Schrodinger Equation
• The Derivative Nonlinear Schrödinger Equation: Global Well-Posedness and Soliton Resolution
• The rational solutions of the mixed nonlinear Schrödinger equation
• Asymptotics of Solutions to the Modified Nonlinear Schrödinger Equation: Solitons on a Non-Vanishing Continuous Background
• Long-time behavior for the Cauchy problem of the 3-component Manakov system
• Long-time asymptotic behavior for the Novikov equation in solitonic regions of space time
• Long-time asymptotics for the Wadati-Konno-Ichikawa equation with the Schwartz initial data