Repelling soliton collisions in coupled SchrÃ¶dinger equations
with negative cross modulation
W. Josh Sonnier - Department of Physics, Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States (email) Abstract: The system of Coupled Nonlinear SchrÃ¶dinger'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: Models, numerical methods,Simulation,Nonlinear stabilities
Received: August 2008; Revised: July 2009; Published: September 2009. |