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Published on: March 19, 2016
Modulational instability in two-component discrete media with cubic-quintic nonlinearity.
B B Baizakov1, A Bouketir, A Messikh
1Physical-Technical Institute, Uzbek Academy of Sciences, 100084 Tashkent, Uzbekistan.
Summary
This study examines cubic-quintic nonlinearity in two-component discrete nonlinear Schrödinger equations. Quintic nonlinearity significantly enhances modulational instability (MI) compared to cubic nonlinearity, impacting Bose-Einstein condensates and optical systems.
Area of Science:
- Nonlinear Optics
- Quantum Physics
- Condensed Matter Physics
Background:
- The discrete nonlinear Schrödinger (DNLS) equation models wave propagation in nonlinear media.
- Cubic and quintic nonlinearities, along with intercomponent couplings, influence system dynamics.
- Modulational instability (MI) is a key phenomenon leading to pattern formation.
Purpose of the Study:
- To investigate the impact of cubic-quintic nonlinearity and intercomponent couplings on the modulational instability (MI) of plane-wave solutions in the two-component DNLS equation.
- To analytically derive conditions for MI onset and growth rates.
- To explore the relevance of these findings to Bose-Einstein condensates (BECs) and optical waveguide arrays.
Main Methods:
- Analytical derivation of modulational instability conditions and growth rates.
- Numerical simulations of the coupled cubic-quintic DNLS equation.
- Comparison of the effects of cubic versus quintic nonlinearities.
Main Results:
- Conditions for the onset of modulational instability were determined.
- The growth rate of small perturbations was analytically derived.
- Quintic nonlinearity was found to have a stronger effect on MI than cubic nonlinearity for equal initial parameters.
- Phase separation in two-component Bose-Einstein condensates under MI was predicted and confirmed via simulations.
Conclusions:
- The study provides a comprehensive analysis of modulational instability in a two-component discrete nonlinear Schrödinger model with cubic-quintic nonlinearity.
- The findings are relevant to understanding phenomena in dense Bose-Einstein condensates and nonlinear optical systems.
- The research highlights the significant role of higher-order nonlinearities in wave dynamics.
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