2013/12/12 by Xin Wang, Yuqi Li, Wang, Xin +3
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1312.3436
openalex publication_date 2013/12/12 · arxiv created 2014/04/28 · arxiv updated 2014/04/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we construct a generalized Darboux transformation to the coupled Hirota equations with high-order nonlinear effects like the third dispersion, self-steepening and inelastic Raman scattering terms. As application, an Nth-order localized wave solution on the plane backgrounds with the same spectral parameter is derived through the direct iterative rule. In particular, some semi-rational, multi-parametric localized wave solutions are obtained: (1) Vector generalization of the first- and the second-order rogue wave solution; (2) Interactional solutions between a dark-bright soliton and a rogue wave, two dark-bright solitons and a second-order rogue wave; (3) Interactional solutions between a breather and a rogue wave, two breathers and a second-order rogue wave. The results further reveal the striking dynamic structures of localized waves in complex coupled systems.