Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations

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2007, 2007(Special): 982-992. doi: 10.3934/proc.2007.2007.982

Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations

M. D. Todorov ^1, and C. I. Christov ^2,

1.	Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria
2.	Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States

Received July 2006 Revised March 2007 Published September 2007

Abstract
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For the Coupled Nonlinear Schrodinger Equations (CNLSE) we construct a conservative fully implicit numerical scheme using complex arithmetic which allows to reduce the computational time fourfold. We obtain various results numerically and investigate the role of the nonlinear and linear coupling. For nontrivial but moderate nonlinear coupling parameter, we find that the polarization of the system changes, but no other effects are present. For large values of the nonlinear coupling parameter, additional (faster) solitons are created during the collision of the initial ones. The linear coupling is shown to manage the self-focusing/dispersion and to make the additional solitons appear for smaller nonlinear coupling. These seem to be new effects, not reported in the literature.

Keywords: NLS-like (nonlinear Schrodinger) equations, Solitons., Conservative numerical schemes, Finite difference methods.

Mathematics Subject Classification: Primary: 65M06, 35Q55 Secondary: 35Q5.

Citation: M. D. Todorov, C. I. Christov. Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations. Conference Publications, 2007, 2007 (Special) : 982-992. doi: 10.3934/proc.2007.2007.982

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