2020/12/31 by Guoqiang Zhang, Liming Ling, Zhenya Yan
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Applied mathematics #Boundary (topology) #Boundary value problem #Component (thermodynamics) #Mathematical analysis #Mathematical physics #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Nonlinear system #Order (exchange) #Physics #Quantum mechanics #Schrödinger equation #math-ph #math.AP #math.MP #nlin.PS #nlin.SI #physics.comp-ph
paper · pdf · doi:10.1007/s00332-021-09735-z
published as Journal of Nonlinear Science 31 (2021) 81 · 42 pages, 7 figures
arxiv created 2020/12/31 · openalex publication_date 2021/08/03 · openalex created_date 2021/08/30 · arxiv updated 2021/11/19 · openalex updated_date 2026/08/05
We first report the first- and higher-order vector Peregrine solitons (alias rational rogue waves) for the any multi-component NLS equations based on the loop group theory, an explicit (n + 1)-multiple eigenvalue of a characteristic polynomial of degree (n + 1) related to the condition of Benjamin-Feir instability, and inverse functions. Particularly, these vector rational rogue waves are parity-time symmetric for some parameter constraints. A systematic and effective approach is proposed to study the asymptotic behaviors of these vector rogue waves such that the decompositions of rogue waves are related to the so-called governing polynomials, which pave a powerful way in the study of vector rogue wave structures of the multi-component integrable systems. The vector rogue waves with maximal amplitudes can be determined via the parameter vectors, which is interesting and useful in the multi-component physical systems.