Discrete four-component massive Thirring model

Abstract

We construct a discrete four-component massive Thirring model (MTM) within the Cauchy matrix framework. A connection between the dependent variables of the discrete four-component MTM and those of the discrete Mikhailov model is established. Taking two successive continuum limits, we first reduce this discrete four-component MTM to its semi-discrete counterpart, and further arrive at the continuous four-component MTM. Solving the determining equation set enables us to construct AKNS-type and KP-type solutions, including explicit soliton solutions and multiple-pole solutions. Imposing the local reduction and nonlocal reduction on the discrete four-component MTM yields the discrete MTM and the reverse-(n,m) discrete MTM, respectively. For these two reduced systems, we prove that the former admits AKNS-type solutions, whereas the latter possesses both AKNS-type and KP-type solutions.