Riemann–Hilbert approach to two-component modified short-pulse system and its nonlocal reductions

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...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2022-09, Vol.32 (9), p.093120-093120
Main Authors: Lv, Cong, Qiu, Deqin, Liu, Q. P.
Format: Article
Language:English
Subjects:
Boundary conditions
Cauchy problems
Defocusing
Mathematical analysis
Short pulses
Solitary waves
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Summary: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.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0088293