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Stabilization of solitons under competing nonlinearities by external potentials
Krzysztof B Zegadlo1, Tomasz Wasak2, Boris A Malomed3
1Faculty of Physics, Warsaw University of Technology, Warsaw, ul. Koszykowa 75, PL-00-662 Warszawa, Poland.
Chaos (Woodbury, N.Y.)
|January 3, 2015
Summary
This study analyzes one-dimensional trapped solitons with competing nonlinearities. We found that Vakhitov-Kolokolov criteria can predict the stability of these solitons in optical and Bose-Einstein condensate systems.
Area of Science:
- Nonlinear Optics
- Quantum Physics
- Soliton Dynamics
Background:
- One-dimensional (1D) trapped solitons are crucial in nonlinear optics and Bose-Einstein condensates.
- Competing nonlinear terms, specifically self-focusing (SF) quintic and self-defocusing (SDF) cubic, present unique challenges in soliton stability.
- Understanding soliton behavior in various trapping potentials is essential for technological applications.
Purpose of the Study:
- To analyze families of 1D trapped solitons generated by competing SF quintic and SDF cubic nonlinearities.
- To investigate soliton behavior under harmonic-oscillator (HO) and delta-functional trapping potentials.
- To assess the applicability of Vakhitov-Kolokolov (VK) and anti-VK criteria for predicting soliton stability.
Main Methods:
- Variational and Thomas-Fermi approximations for approximate solutions under HO potential.
- Full numerical simulations for ground and excited states under HO potential.
- Fully analytical solutions, verified numerically, for the delta-functional potential.
Main Results:
- Existence of both exponentially localized solitons and weakly localized trapped modes for the delta-functional potential.
- Approximate and numerical results for soliton properties under the HO potential.
- Identification of specific soliton families based on the interplay of nonlinear terms and potentials.
Conclusions:
- The Vakhitov-Kolokolov (VK) and anti-VK criteria are applicable for determining the stability of solitons with competing nonlinearities.
- The findings are relevant for optical solitons in photonic media and matter-wave solitons in Bose-Einstein condensates.
- This research provides a theoretical framework for controlling and predicting soliton behavior in complex nonlinear systems.
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