On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations

Details On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations On convergence and stability of a numerical scheme of coupled nonlinear Schrödinger equations

2006-11-14

arxiv.org/abs/math/0611420v1

Mathematics

Numerical Analysis

16 pages, 19 figures, 3 tables

Scientific paper

We consider numerical solution of Coupled Nonlinear Schr\"{o}dinger Equation. We prove stability and convergence in the $L_2$ space for an explicit scheme which estimations is used for implicit scheme and compare both method. As a test we compare numerical solutions of Manakov system with known analytical solitonic solutions and as example of general system - evolution of two impulses with different group velocity (model of pulses interaction in optic fibers). Last example, a rectangular pulse evolution, shows asymptotic behavior typical for Nonlinear Schr\"{o}dinger Equation asymptotics with the same initial condition.

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