Strong coupling of Schrödinger equations: Conservative scheme approach

Authors:
W. J. Sonnier;C. I. Christov
Affiliations:
Department of Mathematics, University of Louisiana at Lafayette, P.O. Box 1010, Lafayette, LA 70504, USA;Department of Mathematics, University of Louisiana at Lafayette, P.O. Box 1010, Lafayette, LA 70504, USA
Venue:
Mathematics and Computers in Simulation
Year:
2005

Citing 1
Cited 4

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Maximum norm error bound of a linearized difference scheme for a coupled nonlinear Schrödinger equations

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Lobatto IIIA-IIIB discretization of the strongly coupled nonlinear Schrödinger equation

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Collision dynamics of elliptically polarized solitons in Coupled Nonlinear Schrödinger Equations

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Local energy-preserving and momentum-preserving algorithms for coupled nonlinear Schrödinger system

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Abstract

The system of coupled nonlinear Schrodinger's equations (CNLSE) is considered and the physical meaning of the coupling terms is identified. The attention is focused on the case of real-valued parameter of linear cross-diffusion. A new analytical solution for the coupled case is found and used as initial condition for the interaction and evolution of two pulses. Conservative numerical scheme and algorithm are devised for the time evolution of solitons in CNLSE. The results show that the coupling term brings into play localized solutions with rotating polarization which in many instances behave as breathers. Both elastic and inelastic collisions are uncovered numerically.