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Sib. Èlektron. Mat. Izv., 2013, Volume 10, Pages 418–435 (Mi semr422)  

This article is cited in 3 scientific papers (total in 3 papers)

Differentical equations, dynamical systems and optimal control

Classes of generalized functional invariant solutions of wave equation. I

M. V. Neshchadimab

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
b Novosibirsk State University

Abstract: Proved that formula Smirnov–Sobolev give all real-valued functional invariant solutions of wave equation in space arbitrary dimension. Proved that solution with many phase functions are essential complex-valued. Considered problem finding of amplitude of generalized functional invariant solution for given phase.

Keywords: wave equation, generalized functional invariant solutions.

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Document Type: Article
UDC: 517.95
MSC: 35L05, 35N10
Received April 19, 2013, published May 21, 2013

Citation: M. V. Neshchadim, “Classes of generalized functional invariant solutions of wave equation. I”, Sib. Èlektron. Mat. Izv., 10 (2013), 418–435

Citation in format AMSBIB
\Bibitem{Nes13}
\by M.~V.~Neshchadim
\paper Classes of generalized functional invariant solutions of wave equation.~I
\jour Sib. \`Elektron. Mat. Izv.
\yr 2013
\vol 10
\pages 418--435
\mathnet{http://mi.mathnet.ru/semr422}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. V. Neshchadim, “Functional-invariant solutions to the Maxwell system”, J. Appl. Industr. Math., 11:1 (2017), 107–114  mathnet  crossref  crossref  mathscinet  elib
    2. M. V. Neschadim, “Obobschennye funktsionalno-invariantnye resheniya volnovogo uravneniya v razmernosti 2”, Sib. zhurn. chist. i prikl. matem., 17:3 (2017), 58–66  mathnet  crossref
    3. L. T. Stepien, “On certain exact solutions for some equations in field theory”, New Trends in Analysis and Interdisciplinary Applications, Trends in Mathematics, eds. P. Dang, M. Ku, T. Qian, L. Rodino, Birkhauser Boston, 2017, 327–335  crossref  mathscinet  zmath  isi
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