The massive Thirring system in the quarter plane

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.

arXiv comment33 pages, 2 figures

References in corpus (7)

• The Nonlinear Schrödinger Equation on the Interval
• The Unified Method: I Non-Linearizable Problems on the Half-Line
• Initial-boundary value problems for integrable evolution equations with $3\times 3$ Lax pairs
• Initial-boundary value problems associated with the Ablowitz-Ladik system
• Initial-boundary value problems for discrete evolution equations: discrete linear Schrodinger and integrable discrete nonlinear Schrodinger equations
• Integrable semi-discretization of the massive Thirring system in laboratory coordinates
• The Ablowitz-Ladik system on a finite set of integers