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TMF, 1994, Volume 99, Number 2, Pages 263–277 (Mi tmf1586)  

This article is cited in 4 scientific papers (total in 4 papers)

Generalized conditional symmetries and exact solutions of non-integrable equations

A. S. Fokasa, Q. M. Liub

a Loughborough University
b Clarkson University

Abstract: We introduce the concept of a generalized conditional symmetry. This concept provides an algorithm for constructing physically important exact solutions of non-integrable equations. Examples include 2-shock and 2-soliton solutions. The existence of such exact solutions for non-integrable equations can be traced back to the relation of these equations with integrable ones. In this sense these exact solutions are remnants of integrability.

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English version:
Theoretical and Mathematical Physics, 1994, 99:2, 571–582

Bibliographic databases:

Language: English

Citation: A. S. Fokas, Q. M. Liu, “Generalized conditional symmetries and exact solutions of non-integrable equations”, TMF, 99:2 (1994), 263–277; Theoret. and Math. Phys., 99:2 (1994), 571–582

Citation in format AMSBIB
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\paper Generalized conditional symmetries and exact solutions of non-integrable equations
\jour TMF
\yr 1994
\vol 99
\issue 2
\pages 263--277
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1308788}
\zmath{https://zbmath.org/?q=an:0850.35097}
\transl
\jour Theoret. and Math. Phys.
\yr 1994
\vol 99
\issue 2
\pages 571--582
\crossref{https://doi.org/10.1007/BF01016141}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1994PV07100013}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. Sergyeyev, “On the classification of conditionally integrable evolution systems in $(1+1)$ dimensions”, J. Math. Sci., 136:6 (2006), 4392–4400  mathnet  crossref  mathscinet  zmath
    2. Tsuchida, T, “Classification of polynomial integrable systems of mixed scalar and vector evolution equations: I”, Journal of Physics A-Mathematical and General, 38:35 (2005), 7691  crossref  mathscinet  zmath  adsnasa  isi
    3. Svetlana Kordyukova, “Nonclassical Approximate Symmetries of Evolution Equations with a Small Parameter”, SIGMA, 2 (2006), 040, 11 pp.  mathnet  crossref  mathscinet  zmath
    4. Barannyk A.F. Barannyk T.A. Yuryk I.I., “Generalized Separation of Variables for Nonlinear Equation U(Tt) = F(U)U(XX) + Af `(U)U(X)(2)”, Rep. Math. Phys., 71:1 (2013), 1–13  isi
  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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