T. Xu and D.E. Pelinovsky

Darboux transformation and soliton solutions of the semi-discrete massive Thirring model

Physics Letters A 383 (2019) 125948 (14 pages)

Abstract:
A one-fold Darboux transformation between solutions of the semi-discrete massive Thirring model is derived using the Lax pair and the dressing method. This transformation is used to find the exact expressions for soliton solutions on zero and nonzero backgrounds. It is shown that the discrete solitons have the same properties as their continuous counterparts.

Keywords:
Massive Thirring model, integrable semi-discretization, soliton solutions, Darboux transformations, modulational stability.