N. Joshi and D.E. Pelinovsky

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


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.

Keywords:
Massive Thirring Model, integrable semi-discretization, Ablowitz-Ladik lattice, Backlund transformation