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Title: A focusing and defocusing semi-discrete complex short-pulse equation and its various soliton solutions
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 )).  more » « less
Award ID(s):
1715991
NSF-PAR ID:
10374228
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume:
477
Issue:
2247
ISSN:
1364-5021
Page Range / eLocation ID:
20200853
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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