Critical and Subcritical Cases of the Toda Shock Problem

Abstract

In this paper we consider the Toda lattice of interacting particles. Physically, this is a one-dimensional lattice of particles interacting with exponential forces,

$${{\dot{x}}_{n}} = {{y}_{n}}$$

(I.1.1a)

$$ {{\dot{y}}_{n}} = {{e}^{{{{x}_{{n - 1}}} - {{x}_{n}}}}} - {{e}^{{{{x}_{n}} - {{x}_{n}} + 1}}}.$$

(I.1.1b)