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Two-dimensional solitons in media with stripe-shaped nonlinearity modulation
Nguyen Viet Hung1, Paweł Ziń, Marek Trippenbach
1Soltan Institute for Nuclear Studies, Hoża 69, PL-00-681 Warsaw, Poland.
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 15, 2011
Summary
We present a model for stable two-dimensional (2D) solitons in nonlinear media. Rectangular stripe profiles support stable solitons, unlike Gaussian profiles, with implications for nonlinear optics and Bose-Einstein condensates (BEC).
Area of Science:
- Nonlinear Optics
- Bose-Einstein Condensates (BEC)
- Mathematical Physics
Background:
- Investigating stable two-dimensional (2D) solitons in media with localized self-attractive nonlinearity is challenging.
- Previous research highlights the difficulty in finding stable solitons in such systems.
Purpose of the Study:
- To introduce and analyze a model of media with cubic attractive nonlinearity along single or double stripes in 2D.
- To determine the conditions for the existence and stability of 2D solitons within this model.
- To explore the influence of stripe profile shape on soliton stability.
Main Methods:
- Variational approximation (VA) to analyze soliton properties.
- Numerical simulations to investigate existence and stability.
- Direct simulations to study soliton collisions.
Main Results:
- Soliton stability critically depends on the stripe's transverse profile: rectangular profiles support stable 2D solitons, while Gaussian profiles lead to instability.
- The VA accurately predicts the shape and stability of single-peak solitons in double-stripe configurations.
- Stable solitons in double rectangular stripes can be symmetric or asymmetric (single-peak) or symmetric (double-peak).
- Soliton collisions can result in intrinsic oscillations, decay, or catastrophic self-focusing (collapse), depending on collision velocity.
Conclusions:
- The transverse shape of the nonlinear stripe is a key factor determining the stability of 2D solitons.
- The developed model and methods provide accurate predictions for soliton behavior in specific nonlinear media.
- The findings have implications for controlling and utilizing solitons in nonlinear optical systems and BECs.
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