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N-soliton collision in the Manakov model | Takayuki Tsuchida
; | Date: |
27 Feb 2003 | Journal: | Prog.Theor.Phys. 111 (2004) 151-182 | Subject: | Exactly Solvable and Integrable Systems; Optics; Mathematical Physics; Quantum Algebra | nlin.SI hep-th math-ph math.MP math.QA physics.optics | Affiliation: | University of Tokyo | Abstract: | 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 $t o mp infty$, 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. | Source: | arXiv, nlin.SI/0302059 | Services: | Forum | Review | PDF | Favorites |
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