American Institute of Mathematical Sciences

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

Repelling soliton collisions in coupled Schrödinger equations with negative cross modulation

W. Josh Sonnier 1, and  C. I. Christov 2,

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.
Keywords: Simulation, numerical methods, Models, Nonlinear stabilities.
Mathematics Subject Classification: Primary: 65C20, 68U20,37M05,65P40.
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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