N-soliton collision in the Manakov model

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dc.creatorTsuchida, Takayuki
dc.date2003-02-27
dc.date2004-02-02
dc.date.accessioned2026-07-07T06:24:30Z
dc.date.available2026-07-07T06:24:30Z
dc.descriptionWe 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 $t \to \mp \infty$, 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.
dc.descriptionLaTeX2e, 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
dc.identifierhttps://arxiv.org/abs/nlin/0302059
dc.identifierhttp://arxiv.org/abs/nlin/0302059
dc.identifierProg.Theor.Phys. 111 (2004) 151-182
dc.identifierdoi:10.1143/PTP.111.151
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/96564
dc.subjectExactly Solvable and Integrable Systems
dc.subjectHigh Energy Physics - Theory
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subjectOptics
dc.titleN-soliton collision in the Manakov model
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