N-soliton collision in the Manakov model

Details N-soliton collision in the Manakov model N-soliton collision in the Manakov model

2003-02-27

arxiv.org/abs/nlin/0302059v4

Prog.Theor.Phys. 111 (2004) 151-182

Nonlinear Sciences

Exactly Solvable and Integrable Systems

LaTeX2e, 33 pages, 3 figures; (v2) typos corrected, sentences improved, references added; (v3) introduction expanded, remarks

Scientific paper

10.1143/PTP.111.151

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 $t \to \mp \infty$, 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.

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