A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
type: Item
instance of: scholarly article
title: A steepest descent method for oscillatory Riemann-Hilbert problems. Asymptotics for the MKdV equation
zbMATH Open document ID: 0771.35042
DOI: 10.2307/2946540
published in: Annals of Mathematics. Second Series
publication date: 1993-06-29T00:00:00Z
review text: We present a new and general approach to analyzing the asymptotics of oscillatory Riemann-Hilbert problems. Such problems arise, in particular, when evaluating the long-time behavior of nonlinear wave equations solvable by the inverse scattering method. We restrict ourselves to the modified Korteweg-de Vries (MKdV) equation \[ y_ t-6y^ 2y_ x+y_{xxx}=0, \qquad -\infty<x<\infty, \qquad t\geq 0, \qquad y(x,t=0)=y_ 0(x), \] but the method extends naturally to the general class of wave equations solvable by the inverse scattering method, such as the KdV, nonlinear Schrödinger (NLS) and Boussinesq equations, and also to ``integrable'' ordinary differential equations such as the Painlevé transcendents.
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 35Q53
Mathematics Subject Classification ID: 35B40
zbMATH DE Number: 224049
zbMATH Keywords: long-time behavior of nonlinear wave equations
zbMATH Keywords: inverse scattering method
Wikidata QID: Q56386738
author: Percy A. Deift
author: X. Zhou
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2307/2946540
OpenAlex ID: W2062565740
description: scientific article