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Zh. Vychisl. Mat. Mat. Fiz., 2008, Volume 48, Number 12, Pages 2151–2162 (Mi zvmmf70)  

This article is cited in 6 scientific papers (total in 6 papers)

The polygonal method for constructing exact solutions to certain nonlinear differential equations describing water waves

M. V. Demina, N. A. Kudryashov, D. I. Sinel'shchikov

Moscow Engineering Physics Institute (State University), Kashirskoe sh. 31, Moscow, 115409, Russia

Abstract: A method is proposed for constructing exact solutions to certain nonlinear differential equations of mathematical physics. Possible applications of this method are illustrated using equations arising in the description of water waves. Exact solutions to the generalized Gardner, Kawahara, and Benjamin–Bona–Mahony equations are constructed.

Key words: nonlinear differential equations of mathematical physics, wave equations, polygonal method for constructing exact solutions.

Full text: PDF file (1089 kB)
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English version:
Computational Mathematics and Mathematical Physics, 2008, 48:12, 2182–2193

Bibliographic databases:

UDC: 519.63
Received: 21.11.2007
Revised: 27.03.2008

Citation: M. V. Demina, N. A. Kudryashov, D. I. Sinel'shchikov, “The polygonal method for constructing exact solutions to certain nonlinear differential equations describing water waves”, Zh. Vychisl. Mat. Mat. Fiz., 48:12 (2008), 2151–2162; Comput. Math. Math. Phys., 48:12 (2008), 2182–2193

Citation in format AMSBIB
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\paper The polygonal method for constructing exact solutions to certain nonlinear differential equations describing water waves
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\issue 12
\pages 2151--2162
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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. Ebadi G., Biswas A., “The $\frac{G'}{G}$ method and topological soliton solution of the $K(m,n)$ equation”, Commun. Nonlinear Sci. Numer. Simul., 16:6 (2011), 2377–2382  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    2. Saha A., “Bifurcation of travelling wave solutions for the generalized KP-NEW equations”, Commun. Nonlinear Sci. Numer. Simul., 17:9 (2012), 3539–3551  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. Kudryashov N.A., Sinelshchikov D.I., “Nonlinear differential equations of the second, third and fourth order with exact solutions”, Appl. Math. Comput., 218:21 (2012), 10454–10467  crossref  mathscinet  zmath  isi  elib  scopus
    4. S. P. Popov, “Effect of cubic nonlinearity on soliton solutions of the Benjamin–Bona–Mahony equation”, Comput. Math. Math. Phys., 53:4 (2013), 477–485  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    5. Comput. Math. Math. Phys., 53:9 (2013), 1371–1376  mathnet  crossref  crossref  isi  elib  elib
    6. Kumar R., Gupta R.K., Bhatia S.S., “Invariant Solutions of Variable Coefficients Generalized Gardner Equation”, Nonlinear Dyn., 83:4 (2016), 2103–2111  crossref  mathscinet  zmath  isi  elib  scopus
  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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