2003/02/28 by Takayuki Tsuchida, T. Tsuchida · 2 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #hep-th #math-ph #math.MP #math.QA #nlin.SI #physics.optics
paper · pdf · doi:10.1143/ptp.111.151
published as Prog.Theor.Phys. 111 (2004) 151-182 · LaTeX2e, 33 pages, 3 figures; (v2) typos corrected, sentences improved, references added; (v3) introduction expanded, remarks on the Yang-Baxter property added below Theorem 3.1 and Theorem 5.4, critical comments made on the recent paper of Kanna and Lakshmanan nlin.SI/0303025 (PRE 67 (2003) 046617), references added and replaced; (v4) grammatical improvements based on proofreading by an English advisor, titles of the references removed (cf. v3), to appear in Prog. Theor. Phys
crossref issued 2004/02/01 · crossref published 2004/02/01 · crossref published-print 2004/02/01 · openalex publication_date 2004/02/01 · arxiv created 2004/02/02 · crossref created 2005/02/28 · openalex created_date 2016/06/24 · crossref deposited 2017/08/24 · crossref indexed 2026/07/26 · openalex updated_date 2026/07/29
We investigate soliton collisions in the Manakov model, which is a system of coupled nonlinear Schroedinger equations that is integrable via the inverse scattering method. Computing the asymptotic forms of the general N-soliton solution in the limits t → ∓ ∞, we elucidate a mechanism that factorizes an N-soliton collision into a nonlinear superposition of N \choose 2 pair collisions with arbitrary order. This removes the misunderstanding that multi-particle effects exist in the Manakov model and provides a new ``set-theoretical'' solution to the quantum Yang-Baxter equation. As a by-product, we also obtain a new nontrivial relation among determinants and extended determinants.