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Repelling soliton collisions in coupled Schrödinger equations with negative cross modulation

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  • The system of Coupled Nonlinear Schrödinger's Equations (CNLSE) is solved numerically by means of a conservative difference scheme. A new kind of repelling collision is discovered for negative values of the cross-modulation coupling parameter, $\alpha_2$. The results show that as the latter becomes increasingly negative, the behavior of the solitons during interaction change drastically. While for $\alpha_2 >0$, the solitons pass through each other, a negative threshold value $\alpha^*_2 < 0$ is found below which the solitons repell each other. This is a novel result for this kind of models and the conservation of momentum for the system of quasi-particles (QPs) is thoroughly investigated.
    Mathematics Subject Classification: Primary: 65C20, 68U20,37M05,65P40.

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