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Compactons in nonlinear Schrödinger lattices with strong nonlinearity management
F Kh Abdullaev1, P G Kevrekidis, M Salerno
1CFTC, Universidade de Lisboa, Avenida Professor Gama Pinto 2, Lisboa 1649-003, Portugal.
Physical Review Letters
|September 28, 2010
Summary
Stable discrete compactons, which are localized nonlinear waves, are demonstrated in modulated discrete nonlinear Schrödinger equations. These compactons can arise from various initial conditions in nonlinear optics and Bose-Einstein condensates.
Area of Science:
- Nonlinear dynamics
- Quantum physics
- Optics
Background:
- The discrete nonlinear Schrödinger equation (DNLS) models wave propagation in discrete systems like optical waveguide arrays and Bose-Einstein condensates.
- Compactons are particle-like, localized nonlinear waves that do not spread over time.
Purpose of the Study:
- To demonstrate the existence of stable discrete compactons in the DNLS equation with fast periodic modulations of nonlinearity.
- To investigate the influence of modulation parameters and field amplitude on interwell tunneling and compacton stability.
Main Methods:
- Averaging technique applied to the DNLS equation with fast time-periodic nonlinearity.
- Analysis of the resulting effective averaged DNLS equation to identify conditions for compacton formation.
- Numerical simulations to confirm the dynamic emergence and stability of compactons.
Main Results:
- Fast periodic modulations of nonlinearity lead to an effective interwell tunneling in the averaged DNLS equation.
- This tunneling is dependent on modulation parameters and field amplitude, introducing nonlinear dispersion.
- Stable single- or multisite discrete compactons can be realized in nonlinear optical and BEC arrays.
Conclusions:
- The study establishes a method for creating stable discrete compactons through nonlinearity modulation.
- These compactons offer a novel platform for studying nonlinear localized phenomena in discrete systems.
- The findings have implications for controlling wave localization in optical and quantum systems.
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