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The massive Thirring system in the quarter plane

Part of: Infinite-dimensional Hamiltonian systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  23 April 2019

Baoqiang Xia
Baoqiang Xia*
Affiliation:
School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou, Jiangsu221116, P. R. China (xiabaoqiang@126.com)
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Abstract

The unified transform method (UTM) or Fokas method 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 in the quarter plane, assuming that the initial and boundary data belong to the Schwartz class. We show that for this integrable model, the UTM is as effective as the IST method: Riemann-Hilbert 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.

Keywords

massive Thirring systeminitial-boundary value problemunified transform methodinverse scattering transform

MSC classification

Primary: 35Q51: Soliton-like equations
Secondary: 37K15: Integration of completely integrable systems by inverse spectral and scattering methods
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 150 , Issue 5 , October 2020 , pp. 2387 - 2416
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Copyright
Copyright © Royal Society of Edinburgh 2019

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