# American Institute of Mathematical Sciences

2009, 2009(Special): 708-718. doi: 10.3934/proc.2009.2009.708

## Repelling soliton collisions in coupled Schrödinger equations with negative cross modulation

 1 Department of Physics, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States 2 Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States

Received  August 2008 Revised  July 2009 Published  September 2009

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.
Citation: W. Josh Sonnier, C. I. Christov. Repelling soliton collisions in coupled Schrödinger equations with negative cross modulation. Conference Publications, 2009, 2009 (Special) : 708-718. doi: 10.3934/proc.2009.2009.708
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