Long-Time Asymptotics for the Korteweg–de Vries Equation via Nonlinear Steepest Descent
By Katrin Grunert, Gerald Teschl. 2008
188 citations recorded by the source corpus.
We apply the method of nonlinear steepest descent to compute the long-time asymptotics of the Korteweg–de Vries equation for decaying initial data in the soliton and similarity region. This paper can be viewed as an expository introduction to this method.
Subfields: Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bb9270509da40162bf3fae6b0932125e54968527
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In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Long-time asymptotics for the Sasa–Satsuma equation via nonlinear steepest descent method (2018, methodology): “This approach has been successfully applied in determining asymptotic formulas for the initial value problems of a number of integrable systems associated with 2× 2 matrix sprectral problems including the mKdV equation [10], the defocusing NLS equation [11], the KdV equation [14], the Hirota equatio”
- On the Asymptotic Stability of N\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}$$\end{document}-Soliton Solutions (2016, methodology): “Our method for dealing with the poles in the Riemann–Hilbert problem follows the ideas in [1,14,29].”