Multihump-Multivalley Soliton Families on a Plane Wave Background in Birefringent Optical Fibers
arXiv:2607.13773
The paper derives exact multihump‑multivalley soliton families on a plane‑wave background in birefringent optical fibers using the two‑component Fokas‑Lenells equations and Darboux transformation, and demonstrates their robustness and distinctive topological features.
Abstract
We obtain a family of multihump-multivalley solitons (MHMVSs) on a plane-wave background in birefringent optical fibers governed by the two-component Fokas-Lenells equations, with exact solutions derived via the Darboux transformation method. The fundamental solutions are systematically classified through their phase diagrams, and higher-order configurations are identified as well. Notably, the construction extends to solitons with arbitrary MHMV structures, a class of solutions previously unreported in two-component integrable systems. Numerical simulations confirm the robustness of these solutions under weak white noise. Furthermore, analysis of their topological structure reveals that the virtual monopole field is determined equally by the intensity zeros and poles of MHMVSs in the complex plane, a feature that has remained unrecognized in previous studies of nonlinear wave topological phases. These findings reveal a previously unknown soliton family on a plane-wave background along with a distinct topological feature within the two-component framework, thereby enriching the broader understanding of topological phases of nonlinear waves.
13 pages,7 figures, 1 table