Numerical Investigation of the Nonlinear Schrödinger Equation with Saturation

Christou, M. A.
October 2008
AIP Conference Proceedings;10/30/2008, Vol. 1067 Issue 1, p105
Academic Journal
We construct an implicit finite difference scheme to investigate numerically the nonlinear Schrödinger equation with saturation (NLSS). We use Newton’s method to linearize the numerical scheme. We examine the propagation, interaction and overtake interaction of soliton solutions of the NLSS. Moreover, we examine the effect of the saturation term on the solution and compare it with the classical case of the cubic nonlinearity without saturation of nonlinearity. We track numerically the conserved properties and the phase shift experienced by the solitons upon collision.


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