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Teoreticheskaya i Matematicheskaya Fizika, 2005, Volume 144, Number 2, Pages 226–233
DOI: https://doi.org/10.4213/tmf1849 (Mi tmf1849) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Stabilization Mechanism for Two-Dimensional Solitons in Nonlinear Parametric Resonance

N. V. Alekseeva

University of Cape Town
Full-text PDF (208 kB) Citations (3)
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DOI: https://doi.org/10.4213/tmf1849
Abstract: We consider a simple model system supporting stable solitons in two dimensions. The system is the parametrically driven damped nonlinear Schrodinger equation, and the soliton stabilizes for sufficiently strong damping. We elucidate the stabilization mechanism by reducing the partial differential equation to a finite-dimensional dynamical system and conclude that the negative feedback loop occurs via enslaving the soliton phase, locked to the driver, to its amplitude and width.
Keywords: Faraday resonance, driven damped nonlinear Schrodinger equation, oscillons, stability.
English version:
Theoretical and Mathematical Physics, 2005, Volume 144, Issue 2, Pages 1075–1080
DOI: https://doi.org/10.1007/s11232-005-0137-3
Bibliographic databases:
Language: Russian
Citation: N. V. Alekseeva, “Stabilization Mechanism for Two-Dimensional Solitons in Nonlinear Parametric Resonance”, TMF, 144:2 (2005), 226–233; Theoret. and Math. Phys., 144:2 (2005), 1075–1080
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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  • https://doi.org/10.4213/tmf1849
  • https://www.mathnet.ru/eng/tmf/v144/i2/p226
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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    References:54
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