On an integrable system related to the relativistic Toda lattice -B\"acklund transformation and integrable discretization

TL;DR

This paper explores an integrable system linked to the relativistic Toda lattice, providing bilinear representations, Bäcklund transformations, a discrete version, and explicit soliton solutions, advancing understanding of discrete integrable systems.

Contribution

It introduces a fully discrete integrable system related to the relativistic Toda lattice, including bilinear forms, Bäcklund transformations, and explicit soliton solutions, which are novel contributions.

Findings

Derived bilinear representation of the system

Obtained Bäcklund transformation and Lax pair for the discrete system

Presented one-soliton solution using Bäcklund transformation

Abstract

We study an integrable system related to the relativistic Toda lattice. The bilinear representation of this lattice is given and the B\"ackulund transformation obtained. A fully discrete version is also introduced with its bilinear B\"acklund transformation and Lax pair. One-soliton solution of the discrete system is presented by use of B\"acklund transformation.