Abstract
Previously the authors developed a geometric method for studying and solving nonlinear equations and systems of equations with partial derivatives. This method is used in this paper to obtain a series of exact solutions to certain nonlinear acoustics equations, as well as to reduce the system of Euler equations to systems of common differential equations.
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References
N. Kh. Ibragimov and O. V. Rudenko, Acoust. Phys. 50, 406 (2004).
A. G. Kudryavtsev and O. A. Sapozhnikov, Acoust. Phys. 57, 311 (2011).
V. Yu. Karasev, Akust. Zh. 41, 928 (1995).
Yu. R. Lapidus and O. V. Rudenko, Akust. Zh. 38, 363 (1992).
O. V. Rudenko, Acoust. Phys. 60, 368 (2014).
N. H. Ibragimov, S. V. Meleshko, and O. V. Rudenko, J. Phys. A: Math. Theor. 44, 315201 (2011).
Rudenko, O.V. and Soluyan, S.I., Nonlinear Acoustic Theory, (Nauka, Moscow, 1975), [in Russian].
O. V. Rudenko, Acoust. Phys. 56, 457 (2010).
L. I. Rubina and O. N. Ul’yanov, Proc. Steklov Inst. Mathem. 261, suppl. 1, 183 (2008).
L. I. Rubina and O. N. Ul’yanov, Tr. Ins. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk 16, 209 (2010).
L. I. Rubina and O. N. Ul’yanov, Tr. Ins. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk 18, 265 (2012).
L. I. Rubina and O. N. Ul’yanov, Sibir. Mathem. J. 53, 872 (2012).
L. I. Rubina and O. N. Ul’yanov, Tr. Ins. Mat. Mekh. Ural. Otd. Ross. Akad. Nauk 20, 238 (2014).
L. I. Rubina and O. N. Ul’yanov, Vestnik Yuzh.-Ural. Gos. Univ. Ser. Matem. Mekh. Fiz. 5, 52 (2013).
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Original Russian Text © L.I. Rubina, O.N. Ul’yanov, 2015, published in Akusticheskii Zhurnal, 2015, Vol. 61, No. 5, pp. 576–582.
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Rubina, L.I., Ul’yanov, O.N. On solving certain nonlinear acoustics problems. Acoust. Phys. 61, 527–533 (2015). https://doi.org/10.1134/S1063771015050152
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DOI: https://doi.org/10.1134/S1063771015050152