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Conservative numerical scheme in complex arithmetic for coupled nonlinear Schrödinger equations

Pages: 982 - 992, Issue Special, September 2007

 Abstract        Full Text (651.2K)              

M. D. Todorov - Department of Differential Equations, Faculty of Applied Mathematics and Informatics, Technical University of Sofia, 1000 Sofia, Bulgaria (email)
C. I. Christov - Department of Mathematics, University of Louisiana at Lafayette, Lafayette, LA 70504-1010, United States (email)

Abstract: 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:  Finite difference methods, Conservative numerical schemes, NLS-like (nonlinear Schrodinger) equations, Solitons.
Mathematics Subject Classification:  Primary: 65M06, 35Q55 Secondary: 35Q51.

Received: July 2006;      Revised: March 2007;      Published: September 2007.