Long-Time Asymptotics of the Toda Lattice for Decaying Initial Data Revisited

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.

41 pages

References in corpus (3)

• The Fermi-Pasta-Ulam "numerical experiment": history and pedagogical perspectives
• Stability of Periodic Soliton Equations under Short Range Perturbations
• Inverse Scattering Transform for the Toda Hierarchy with Quasi-Periodic Background

Cited by in corpus (23)

• Long-Time Asymptotics for the Camassa-Holm Equation
• Lecture notes on Generalised Hydrodynamics
• Long-Time Asymptotics for the Korteweg-de Vries Equation via Nonlinear Steepest Descent
• Generalised hydrodynamics of the classical Toda system
• Long-Time Asymptotics for the Korteweg-de Vries Equation with Steplike Initial Data
• Stability of the periodic Toda lattice under short range perturbations
• Stability of the Periodic Toda Lattice in the Soliton Region
• Inverse scattering transform for the Toda hierarchy with steplike finite-gap backgrounds
• Long-Time Asymptotics of Perturbed Finite-Gap Korteweg-de Vries Solutions
• On the Spatial Asymptotics of Solutions of the Toda Lattice
• On the evolution of scattering data under perturbations of the Toda lattice
• Long-time asymptotic behavior for the discrete defocusing mKdV equation
• The Robin problem for the nonlinear Schrödinger equation on the half-line
• Long-Time Asymptotics for the Toda Shock Problem: Non-Overlapping Spectra
• Wave phenomena of the Toda lattice with steplike initial data
• Lieb-Robinson Bounds for the Toda Lattice
• $L^2$ Sobolev space bijectivity of the scattering-inverse scattering transforms related to defocusing Ablowitz-Ladik systems
• Properties of the Scattering Matrix and Dispersion Estimates for Jacobi Operators
• Scattering theory with finite-gap backgrounds: Transformation operators and characteristic properties of scattering data
• Stability of the Periodic Toda Lattice: Higher Order Asymptotics
• Long-time asymptotics for the derivative nonlinear Schrödinger equation on the half-line
• Discrete integrable systems, Darboux transformations, and Yang-Baxter maps
• Riemann-Hilbert Theory without local Parametrix Problems: Applications to Orthogonal Polynomials