Long-Time Asymptotics for the Korteweg–de Vries Equation via Nonlinear Steepest Descent

2008/07/31 by Katrin Grunert, Gerald Teschl · 4 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Descent (aeronautics) #Gradient descent #Korteweg–de Vries equation #Method of steepest descent #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Similarity (geometry) #Soliton #math-ph #math.AP #math.MP #nlin.SI

paper · pdf · doi:10.1007/s11040-009-9062-2

published as Math. Phys. Anal. Geom. 12, 287-324 (2009) · 31 pages

openalex publication_date 2009/07/02 · arxiv created 2009/07/13 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

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.

Citations

• Long-time asymptotics for the Toda lattice in the soliton region
• Method for Solving the Korteweg-deVries Equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• Inverse scattering on the line
• A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation

Cited by

• Long-time asymptotics of a full arbitrary-genus dark soliton gas for the defocusing nonlinear Schrodinger equation
• Long-time asymptotics of the coupled nonlinear Schödinger equation in a weighted Sobolev space
• Numerical inverse scattering transform for the coupled modified Korteweg-de Vries equation
• Korteweg–De Vries equation [wikipedia]

Related

• Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data
• Long-time asymptotic analysis of the Korteweg-de Vries equation via the dbar steepest descent method: The Soliton region
• Long-Time Asymptotics for the Camassa-Holm Equation
• Long-time asymptotics for the Korteweg-de Vries equation with integrable reflectionless initial data
• Long time behavior of solutions to the mKdV