2019/01/08 by Bao‐Feng Feng, Liming Ling, Feng, Bao-Feng +3
Mathematics · Physics and Astronomy · #35Q58 #39A10 #Advanced Mathematical Physics Problems #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1901.02388
openalex publication_date 2019/01/08 · openalex created_date 2019/01/25 · openalex updated_date 2026/07/28
In this paper, we are concerned with a a semi-discrete complex short pulse (CSP) equation of both focusing and defocusing types, which can be viewed as an analogue to the Ablowitz-Ladik (AL) lattice in the ultra-short pulse regime. By using a generalized Darboux transformation method, various solutions to this newly integrable semi-discrete equation are studied with both zero and nonzero boundary conditions. To be specific, for the focusing CSP equation, the multi-bright solution (zero boundary condition), multi-breather and high-order rogue wave solutions (nonzero boudanry conditions) are derived, while for the defocusing CSP equation with nonzero boundary condition, 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 (see Physica D, 327 13-29 and Phys. Rev. E 93 052227)