Inverse scattering transform for the complex short-pulse equation by a Riemann–Hilbert approach

Authors

Barbara Prinari
A. David Trubatch
Bao-Feng Feng, The University of Texas Rio Grande ValleyFollow

Document Type

Article

Publication Date

9-17-2020

Abstract

t In this paper, we develop the inverse scattering transform (IST) for the complex short-pulse equation (CSP) on the line with zero boundary conditions at space infinity. The work extends to the complex case the Riemann–Hilbert approach to the IST for the real short-pulse equation proposed by A. Boutet de Monvel, D. Shepelsky and L. Zielinski in 2017. As a byproduct of the IST, soliton solutions are also obtained. Unlike the real SPE, in the complex case discrete eigenvalues are not necessarily restricted to the imaginary axis, and, as consequence, smooth 1-soliton solutions exist for any choice of discrete eigenvalue k1 ∈ C with Im k1 < |Re k1|. The 2-soliton solution is obtained for arbitrary eigenvalues k1, k2, providing also the breather solution of the real SPE in the special case k2 = −k∗

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Recommended Citation

Prinari, Barbara, A. David Trubatch, and Bao-Feng Feng. "Inverse scattering transform for the complex short-pulse equation by a Riemann–Hilbert approach." The European Physical Journal Plus 135, no. 9 (2020): 717. https://doi.org/10.1140/epjp/s13360-020-00714-z

Publication Title

The European Physical Journal Plus

DOI

10.1140/epjp/s13360-020-00714-z