Abstract
The paper presents a concrete study of the existence of generalized and potential symmetries for the 1+1 dimensional version of the Rudenko-Robsman equation, an interesting fourth-order partial differential equation that describes the evolution of nonlinear waves in a dispersive medium. As the main results, the existence of a two-parameter algebra of generalized symmetries and of an infinite-dimensional algebra when potential symmetries are taken into account is proven.
[1] G. Bluman, S. Kumei, Symmetries of Differential Equations (Springer-Verlag, New York, 1989) 10.1007/978-1-4757-4307-4Search in Google Scholar
[2] N. Ibragimov, Transformation Groups Applied to Mathematical Physics (D. Reidel, Boston, 1985) 10.1007/978-94-009-5243-0Search in Google Scholar
[3] P. Olver, Applications of Lie Groups to Differential Equations (Springer-Verlag, New York, 1993) 10.1007/978-1-4612-4350-2Search in Google Scholar
[4] A. D. Polyanin, V. F. Zaitsev, Hanbook of Nonlinear Partial Differntial Equations (Chapman and Hall/CRC Press Company, Boca Raton, 2004) 10.1201/9780203489659Search in Google Scholar
[5] A. Boldea, C. R. Boldea, Annals of theWest University of Timisoara, Physics Series 48, 101 (2006) Search in Google Scholar
[6] R. Cimpoiasu, R. Constantinescu, Int. J. Theor. Phys. 45, 1785 (2006) http://dx.doi.org/10.1007/s10773-006-9142-z10.1007/s10773-006-9142-zSearch in Google Scholar
[7] R. Cimpoiasu, R. Constantinescu, Physics Annals of the University of Craiova 18, 73 (2008) Search in Google Scholar
[8] O. V. Rudenko, V. A. Robsman, Dokl. Phys. 384, 735 (2002) Search in Google Scholar
[9] O. V. Rudenko, Phys.-Usp.+ 49, 69, (2006) http://dx.doi.org/10.1070/PU2006v049n01ABEH00587610.1070/PU2006v049n01ABEH005876Search in Google Scholar
[10] M. V. Aver’yanov, M. S. Basova, V. A. Khokhlova, Akustičskij Zurnal 51, 581 (2005) Search in Google Scholar
[11] V. Gusev, Ultrasonics 44, 1335 (2006) http://dx.doi.org/10.1016/j.ultras.2006.05.01210.1016/j.ultras.2006.05.012Search in Google Scholar PubMed
[12] L. A. Ostrovsky, O. V. Rudenko, Acoust. Phys.+, DOI:10.1134/S1063771009060049 10.1134/S1063771009060049Search in Google Scholar
[13] M. L. Gandarias, Nonlinear Anal.-Theor. 71, e1826 (2009) http://dx.doi.org/10.1016/j.na.2009.02.07810.1016/j.na.2009.02.078Search in Google Scholar
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