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Contemporary Mathematics. Fundamental Directions, 2006, Volume 15, Pages 59–75 (Mi cmfd40)  
This article is cited in 2 scientific papers (total in 2 papers)

Nonlocal integrals and conservation laws in the theory of nonlinear solitons

R. I. Bogdanovab

a M. V. Lomonosov Moscow State University
b G I. Budker Institute of Nuclear Physics, Siberian Branch of Russian Academy of Sciences
Full-text PDF (242 kB) Citations (2)
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Abstract: It is natural to investigate properties of solutions to nonstationary linear equations of mathematical physics by means of time-invariant spaces of linear functionals. In the framework of this approach, there appear nonlinear (nonstationary) partial differential equations (dual to original ones) admitting nontrivial groups of self-similarities. The superposition principle in the space of solutions to an original equation can be reproduced for the dual equation in the form of convolutions of kernels of linear functionals. The corresponding construction is applied to the Schrödinger equation on the line, where the ideas of quantum mechanics allows one to understand this new approach.
English version:
Journal of Mathematical Sciences, 2008, Volume 149, Issue 4, Pages 1400–1416
DOI: https://doi.org/10.1007/s10958-008-0073-5
Bibliographic databases:
UDC: 517.958
Language: Russian
Citation: R. I. Bogdanov, “Nonlocal integrals and conservation laws in the theory of nonlinear solitons”, Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14–21, 2005). Part 1, CMFD, 15, PFUR, M., 2006, 59–75; Journal of Mathematical Sciences, 149:4 (2008), 1400–1416
Citation in format AMSBIB
\Bibitem{Bog06}
\by R.~I.~Bogdanov
\paper Nonlocal integrals and conservation laws in the theory of nonlinear solitons
\inbook Proceedings of the Fourth International Conference on Differential and Functional-Differential Equations (Moscow, August 14--21, 2005). Part~1
\serial CMFD
\yr 2006
\vol 15
\pages 59--75
\publ PFUR
\publaddr M.
\mathnet{http://mi.mathnet.ru/cmfd40}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2336429}
\transl
\jour Journal of Mathematical Sciences
\yr 2008
\vol 149
\issue 4
\pages 1400--1416
\crossref{https://doi.org/10.1007/s10958-008-0073-5}
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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