Stability of Waves in Multi-component DNLS system

Details Stability of Waves in Multi-component DNLS system Stability of Waves in Multi-component DNLS system

2007-03-06

arxiv.org/abs/nlin/0703008v1

Nonlinear Sciences

Pattern Formation and Solitons

to appear Journal of Physics A: Mathematical and Theoretical

Scientific paper

10.1088/1751-8113/40/17/011

In this work, we systematically generalize the Evans function methodology to address vector systems of discrete equations. We physically motivate and mathematically use as our case example a vector form of the discrete nonlinear Schrodinger equation with both nonlinear and linear couplings between the components. The Evans function allows us to qualitatively predict the stability of the nonlinear waves under the relevant perturbations and to quantitatively examine the dependence of the corresponding point spectrum eigenvalues on the system parameters. These analytical predictions are subsequently corroborated by numerical computations.

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