Systematic construction of multicomponent optical solitons

Abstract

A systematic method is presented to construct multicomponent optical solitons for the system governed by the vector nonlinear Schr\"odinger equation. By solving the characteristic eigenvalue problem, we obtain a general n-component soliton solution in the presence of nonzero background fields. In the two-component case, we show that this general solution not only includes previously known soliton solutions, e.g., bright-bright, dark-bright, dark-dark pair solitons for self-focusing or self-defocusing media, but depending on the choice of parameters it also exhibits different types of soliton solution. In particular, we obtain a general dark-bright type solution in a self-focusing medium, which describes a breakup of a dark-bright pair into another dark-bright pair and an ``oscillating'' soliton, or the reverse fusing process. In the case of a self-defocusing medium, we generalize the previously known static dark-dark pair and show that a general dark-dark pair is non-static and oscillates periodically through exchanging energies between two components. It is shown that the static case arises when the complex soliton parameter is restricted to a pure imaginary number. We address about the criterion for testing singularity in a general solution in terms of solution parameters, and also about the non-Abelian $\mathrm{SU}(n)$ symmetry of the system.