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Teoreticheskaya i Matematicheskaya Fizika, 2009, Volume 160, Number 1, Pages 229–239
DOI: https://doi.org/10.4213/tmf6394 (Mi tmf6394) 		 
This article is cited in 12 scientific papers (total in 12 papers)

Madelung fluid description of the generalized derivative nonlinear Schrödinger equation: Special solutions and their stability

A. Visinescua, D. Grecua, R. Fedeleb, S. De Nicolac

a National Institute for Physics and Nuclear Engineering
b Università degli Studi di Napoli Federico II
c Istituto di Cibernetica "Eduardo Caianiello"
Full-text PDF (380 kB) Citations (12)
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DOI: https://doi.org/10.4213/tmf6394
Abstract: A correspondence between the families of generalized nonlinear Schrödinger (NLS) equations and generalized KdV equations was recently found using a Madelung fluid description. We similarly consider a special derivative NLS equation. We find a number of solitary waves and periodic solutions (expressed in terms of elliptic Jacobi functions) for a motion with a stationary profile current velocity. We study the stability of a bright solitary wave (ground state) by conjecturing that the Vakhitov–Kolokolov criterion is applicable.
Keywords: nonlinear partial differential equation, generalized nonlinear Schrödinger equation, generalized Korteweg–de Vries equation, Madelung fluid description.
English version:
Theoretical and Mathematical Physics, 2009, Volume 160, Issue 1, Pages 1066–1074
DOI: https://doi.org/10.1007/s11232-009-0098-z
Bibliographic databases:
Language: Russian
Citation: A. Visinescu, D. Grecu, R. Fedele, S. De Nicola, “Madelung fluid description of the generalized derivative nonlinear Schrödinger equation: Special solutions and their stability”, TMF, 160:1 (2009), 229–239; Theoret. and Math. Phys., 160:1 (2009), 1066–1074
Citation in format AMSBIB
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\by A.~Visinescu, D.~Grecu, R.~Fedele, S.~De Nicola
\paper Madelung fluid description of the~generalized derivative nonlinear Schr\"odinger equation: Special solutions and their stability
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\pages 229--239
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\transl
\jour Theoret. and Math. Phys.
\yr 2009
\vol 160
\issue 1
\pages 1066--1074
\crossref{https://doi.org/10.1007/s11232-009-0098-z}
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  • https://doi.org/10.4213/tmf6394
  • https://www.mathnet.ru/eng/tmf/v160/i1/p229
    • This publication is cited in the following 12 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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