Abstract

A new interest in spatial solitions has arisen and it is important to make as much analytical progress as possible, in order to expose the fundamental physics. Hence a mathematical approach is adopted here that begins with the following, general, form of coupled nonlinear Schrodinger equations^[1] (excluding saturation and diffusion) where j = 1,2, Ψ_j is a slowly varying light field envelope, k is the linear coupling strenght and β measures the cross-phase modulation. This is the first time that this general coupling has been studied mathematically. Particular values^[1,2] of β and k (β = 1, k = 0; β = 0, k ≠ 0) have been investigated mathematically, however, and a number of cases (β = 0, k ≠ 0; β ≠ 0, k ≠ 0) have been studied numerically. For β = 1 the equations are integrable by the inverse scattering method.^[4,5] In this paper we develop a comprehensive mathematical theory and consider spatial soliton interactions. We study their combined field in the form of multisoliton potentials.

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