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Teoreticheskaya i Matematicheskaya Fizika, 2014, Volume 179, Number 1, Pages 78–89
DOI: https://doi.org/10.4213/tmf8568 (Mi tmf8568) 		 
This article is cited in 13 scientific papers (total in 13 papers)

Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation

D. E. Pelinovskyab, E. A. Ruvinskayaa, O. E. Kurkinaac, B. Deconinckd

a Nizhny Novgorod State Technical University, Nizhny Novgorod, Russia
b Department of Mathematics and Statistics, McMaster University, Hamilton, Ontario, Canada
c Higher School of Economics, Nizhny Novgorod, Russia
d Department of Applied Mathematics, University of Washington, Seattle, WA, USA
Full-text PDF (734 kB) Citations (13)
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DOI: https://doi.org/10.4213/tmf8568
Abstract: We prove that line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation are unstable under transverse perturbations of arbitrarily small periods, i.e., short waves. The analysis is based on the construction of Jost functions for the continuous spectrum of Schrödinger operators, the Sommerfeld radiation conditions, and the Lyapunov–Schmidt decomposition. We derive precise asymptotic expressions for the instability growth rate in the limit of short periods.
Keywords: nonlinear Schrödinger equation, soliton, transverse instability, Lyapunov–Schmidt decomposition, Fermi's golden rule.
Received: 24.06.2013
English version:
Theoretical and Mathematical Physics, 2014, Volume 179, Issue 1, Pages 452–461
DOI: https://doi.org/10.1007/s11232-014-0154-1
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: D. E. Pelinovsky, E. A. Ruvinskaya, O. E. Kurkina, B. Deconinck, “Short-wave transverse instabilities of line solitons of the two-dimensional hyperbolic nonlinear Schrödinger equation”, TMF, 179:1 (2014), 78–89; Theoret. and Math. Phys., 179:1 (2014), 452–461
Citation in format AMSBIB
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    • This publication is cited in the following 13 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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