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Teoreticheskaya i Matematicheskaya Fizika, 1985, Volume 65, Number 2, Pages 271–284 (Mi tmf5099)  
This article is cited in 5 scientific papers (total in 5 papers)

Nonlinear model of Schrödinger type: Conservation laws, Hamiltonian structure, and complete integrability

N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, A. M. Kurbatov, V. G. Samoilenko
Full-text PDF (1355 kB) Citations (5)
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Abstract: A method is proposed for finding Lax type representations for nonlinear evolution (one-dimensional) equations of mathematical physics. It is shown that the Schrödinger type nonlinear model $\psi_t-i\psi_{xx}+2|\psi|^2\psi_x=0$ admits a Lax-type representation and is a Hamiltonian completely integrable dynamical system. Exact quasiperiodic (finite-gap, i.e  having only a finite number of stability bands in its spectrum) solutions of this system are obtained in terms of Riemann theta functions.
Received: 26.12.1984
English version:
Theoretical and Mathematical Physics, 1985, Volume 65, Issue 2, Pages 1154–1164
DOI: https://doi.org/10.1007/BF01017940
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: N. N. Bogolyubov (Jr.), A. K. Prikarpatskii, A. M. Kurbatov, V. G. Samoilenko, “Nonlinear model of Schrödinger type: Conservation laws, Hamiltonian structure, and complete integrability”, TMF, 65:2 (1985), 271–284; Theoret. and Math. Phys., 65:2 (1985), 1154–1164
Citation in format AMSBIB
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\paper Nonlinear model of Schr\"odinger type: Conservation laws, Hamiltonian structure, and complete integrability
\jour TMF
\yr 1985
\vol 65
\issue 2
\pages 271--284
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=823666}
\zmath{https://zbmath.org/?q=an:0618.35113}
\transl
\jour Theoret. and Math. Phys.
\yr 1985
\vol 65
\issue 2
\pages 1154--1164
\crossref{https://doi.org/10.1007/BF01017940}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1985C929000011}
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  • https://www.mathnet.ru/eng/tmf/v65/i2/p271
    • This publication is cited in the following 5 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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    Abstract page:509
    Full-text PDF :150
    References:66
    First page:2
     
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