Integrable semi-discretization of the massive Thirring system in laboratory coordinates

TL;DR

This paper introduces the first integrable semi-discretization of the massive Thirring system in laboratory coordinates, linking it to the Ablowitz-Ladik lattice through Bäcklund transformations.

Contribution

It presents a novel integrable semi-discretization of the massive Thirring system in laboratory coordinates using Bäcklund transformations and the Ablowitz-Ladik lattice.

Findings

First integrable semi-discretization in laboratory coordinates

Connection established with Ablowitz-Ladik lattice

Derivation of the Lax system for the discretization

Abstract

Several integrable semi-discretizations are known in the literature for the massive Thirring system in characteristic coordinates. We present for the first time an integrable semi-discretization of the massive Thirring system in laboratory coordinates. Our approach relies on the relation between the continuous massive Thirring system and the Ablowitz-Ladik lattice. The Backlund transformation for solutions to the Ablowitz-Ladik lattice and the time evolution of the massive Thirring system in laboratory coordinates are combined together in the derivation of the Lax system for the integrable semi-discretization of the massive Thirring system.