Explicit One-Soliton Solutions of the 1+1 Dimensional Toda Molecule Equation and Their Large Molecule Limit of the Infinite Toda Lattice

Abstract

We have obtained the explicit one-soliton solutions of the 1+1 dimensional Toda molecule equation, (∂⁄∂t)²log V(n, t)−V(n+1, t)+2V(n, t)−V(n−1, t)=0, consisting of arbitrary number of particles which satisfy the molecule boundary condition V(n, t)=0 at n=−M′ and M″ (M′, M″≡arbitrary positive integer constants). It has been shown that for the properly chosen values of arbitrary constant parameters and the large molecule limit, the present Toda molecule one-soliton solutions actually reproduce the well known infinite Toda lattice one-soliton solutions.