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Riemann-Hilbert approach to two-component modified short-pulse system and its nonlocal reductions
Cong Lv1, Deqin Qiu1, Q P Liu1
1Department of Mathematics, China University of Mining and Technology, Beijing 100083, People's Republic of China.
Abstract:
In this paper, a Riemann-Hilbert approach to a two-component modified short-pulse (mSP) system on the line with zero boundary conditions is developed. A parametric representation of the solution to the related Cauchy problem is obtained. Four nonlocal integrable reductions, namely, the real reverse space-time nonlocal focusing and defocusing mSP equations and the complex reverse space-time nonlocal focusing and defocusing mSP equations, are studied in detail. For each case, soliton solutions are presented, and, unlike their local counterparts, the nonlocal equations exhibit certain novel properties induced by the impact of nonlocality.
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