N-Soliton Collision in the Manakov Model

Abstract

We investigate soliton collisions in the Manakov model, which is a system of coupled nonlinear Schrödinger 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 (2N) 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.