School of Mathematical & Statistical Sciences Faculty Publications and Presentations

A focusing and defocusing semi-discrete complex short-pulse equation and its various soliton solutions

Document Type

Article

Publication Date

3-3-2021

Abstract

In this paper, we are concerned with a semi-discrete complex short-pulse (sdCSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz–Ladik lattice in the ultra-short-pulse regime. By using a generalized Darboux transformation method, various soliton solutions to this newly integrable semi-discrete equation are studied with both zero and non-zero boundary conditions. To be specific, for the focusing sdCSP equation, the multi-bright solution (zero boundary conditions), multi-breather and high-order rogue wave solutions (non-zero boundary conditions) are derived, while for the defocusing sdCSP equation with non-zero boundary conditions, the multi-dark soliton solution is constructed. We further show that, in the continuous limit, all the solutions obtained converge to the ones for its original CSP equation (Ling et al. 2016 Physica D 327, 13–29 (doi:10.1016/j.physd.2016.03.012); Feng et al. 2016 Phys. Rev. E 93, 052227 (doi:10.1103/PhysRevE.93.052227)).

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© 2021 The Author(s)

Publication Title

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

DOI

10.1098/rspa.2020.0853

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