Toda Lattice Models with Boundary

TL;DR

This paper studies soliton solutions in Toda lattice models with boundaries, explicitly constructing solutions that satisfy boundary conditions using Hirota's method, and introduces a symmetric boundary condition via two-soliton solutions.

Contribution

It provides explicit boundary solutions for Toda lattice models and demonstrates how to incorporate symmetric boundary conditions using known soliton solutions.

Findings

Explicit boundary solutions for Toda lattice models.

Introduction of Z_infinity-symmetric boundary condition.

Methodology for constructing boundary solutions using Hirota's method.

Abstract

We consider the soliton solutions in 1- and (1+1)-dimensional Toda lattice models with a boundary. We make use of the solutions already known on a full line by means of the Hirota's method. We explicitly construct the solutions satisfying the boundary conditions. The ${\bf Z}_{\infty}$-symmetric boundary condition can be introduced by the two-soliton solutions naturally.