LONG-TIME ASYMPTOTICS OF THE TODA LATTICE FOR DECAYING INITIAL DATA REVISITED

2008/04/30 by Helge Krueger, HELGE KRÜGER, Gerald Teschl +1
Mathematics · Physics and Astronomy · #Differential Equations and Numerical Methods #Initial value problem #Lattice (music) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Soliton #Toda lattice #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1142/s0129055x0900358x

published as Rev. Math. Phys. 21:1, 61-109 (2009) · 41 pages

openalex publication_date 2009/02/01 · arxiv created 2009/03/02 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The purpose of this article is to give a streamlined and self-contained treatment of the long-time asymptotics of the Toda lattice for decaying initial data in the soliton and in the similarity region via the method of nonlinear steepest descent.

Citations

• Toda flows with infinitely many variables
• Method for Solving the Korteweg-deVries Equation
• Interaction of "Solitons" in a Collisionless Plasma and the Recurrence of Initial States
• A Steepest Descent Method for Oscillatory Riemann--Hilbert Problems. Asymptotics for the MKdV Equation
• Integrals of nonlinear equations of evolution and solitary waves
• The Fermi–Pasta–Ulam ‘numerical experiment’: history and pedagogical perspectives
• Theory of Nonlinear Lattices