The massive Thirring system in the quarter plane

TL;DR

This paper demonstrates that the unified transform method effectively solves the initial-boundary value problem for the massive Thirring model in the quarter plane, avoiding unknown boundary values and matching the inverse scattering transform's effectiveness.

Contribution

It shows that for the massive Thirring model, the UTM can be formulated without unknown boundary data, aligning its effectiveness with the inverse scattering transform.

Findings

UTM formulated without unknown boundary values

RH problems have explicit (x,t)-dependence

Method matches IST effectiveness for this model

Abstract

The unified transform method (UTM) for analyzing initial-boundary value (IBV) problems provides an important generalization of the inverse scattering transform (IST) method for analyzing initial value problems. In comparison with the IST, a major difficulty of the implementation of the UTM in general is the involvement of unknown boundary values. In this paper we analyze the IBV problem for the massive Thirring model posed in the quarter plane. We show for this integrable model, the UTM is as effective as the IST method: the Riemann-Hilbert (RH) problems we formulated for such a problem have explicit (x,t)-dependence and depend only on the given initial and boundary values; they do not involve additional unknown boundary values.