Stability of Waves in Multi-component DNLS system

Abstract

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.

to appear Journal of Physics A: Mathematical and Theoretical

References in corpus (7)

• Theory of Nonlinear Matter Waves in Optical Lattices
• Pattern Forming Dynamical Instabilities of Bose-Einstein Condensates: A Short Review
• Families of Matter-Waves for Two-Component Bose-Einstein Condensates
• Vortices in Bose-Einstein Condensates: Some Recent Developments
• Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves
• Static and rotating domain-wall crosses in Bose-Einstein condensates
• Resonant and Non-Resonant Modulated Amplitude Waves for Binary Bose-Einstein Condensates in Optical Lattices