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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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\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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Linking options:
  • https://www.mathnet.ru/eng/tmf6394
  • https://doi.org/10.4213/tmf6394
  • https://www.mathnet.ru/eng/tmf/v160/i1/p229
    • This publication is cited in the following 12 articles:
    1. Yu-Lan Ma, Bang-Qing Li, “Phase transitions of lump wave solutions for a (2+1)-dimensional coupled Maccari system”, Eur. Phys. J. Plus, 139:1 (2024)  crossref
    2. Yong Wu, Miguel Vivas-Cortez, Hamood Ur Rehman, El-Sayed M. Sherif, Abdul Rashid, “Bifurcation study, phase portraits and optical solitons of dual-mode resonant nonlinear Schrodinger dynamical equation with Kerr law non-linearity”, Heliyon, 10:15 (2024), e34416  crossref
    3. Javid A., Seadawy A.R., Raza N., “Dual-Wave of Resonant Nonlinear Schrodinger'S Dynamical Equation With Different Nonlinearities”, Phys. Lett. A, 407 (2021), 127446  crossref  mathscinet  isi
    4. O. O. Pokutnyi, “Boundary-Value Problems for the Evolutionary Schrödinger Equation. I”, J Math Sci, 249:4 (2020), 647  crossref
    5. Heim D.M., “Recursive Formulation of Madelung Continuity Equation Leads to Propagation Equation”, J. Math. Phys., 59:12 (2018), 122101  crossref  mathscinet  zmath  isi  scopus
    6. Grecu D., Grecu A.T., Visinescu A., “Madelung Fluid Description of a Coupled System of Derivative NLS Equations”, Rom. J. Phys., 57:1-2 (2012), 180–191  mathscinet  isi
    7. Anca Visinescu, Dan Grecu, Renato Fedele, Sergio De Nicola, “Periodic and Solitary Wave Solutions of Two Component Zakharov–Yajima–Oikawa System, Using Madelung's Approach”, SIGMA, 7 (2011), 041, 11 pp.  mathnet  crossref  mathscinet
    8. Visinescu A., “Bright-Dark Soliton Interaction in a Multi-Mode Optical Fiber and the Completely Integrable Zakharov-Yajima-Oikawa System”, Physics Conference (Tim-10), AIP Conference Proceedings, 1387, eds. Bunoiu M., Malaescu I., Amer Inst Physics, 2011  crossref  isi  scopus
    9. Grecu D., Fedele R., De Nicola S., Grecu A.T., Visinescu A., “Periodic and solitary wave solutions of generalized nonlinear Schrtsdinger equation using a Madelung fluid description”, Romanian J. Phys., 55:9-10 (2010), 980–994  mathscinet  zmath  isi  elib
    10. Grecu D., Visinescu A., Fedele R., De Nicola S., “Periodic and stationary wave solutions of coupled NLS equations”, Romanian J. Phys., 55:5-6 (2010), 585–600  mathscinet  zmath  isi  elib
    11. Fedele R., De Nicola S., Jovanovic D., Grecu D., Visinescu A., “On the mapping connecting the cylindrical nonlinear von Neumann equation with the standard von Neumann equation”, Journal of Plasma Physics, 76:3-4 (2010), 645–653  crossref  adsnasa  isi  scopus
    12. Fedele R., De Nicola S., Grecu D., Visinescu A., Shukla P.K., “Some mathematical aspects of the correspondence between the generalized nonlinear Schrodinger equation and the generalized Korteweg-de Vries equation”, New Developments in Nonlinear Plasma Physics, AIP Conference Proceedings, 1188, 2009, 365–379  crossref  adsnasa  isi  scopus
    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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