Nadjafikhah, Mehdi; Shirvani-Sh, Vahid Lie symmetry analysis of Kudryashov-Sinelshchikov equation. (English) Zbl 1236.35155 Math. Probl. Eng. 2011, Article ID 457697, 9 p. (2011). Summary: The Lie symmetry method is performed for the fifth-order nonlinear evolution Kudryashov-Sinelshchikov equation. We find one- and two-dimensional optimal systems of Lie subalgebras. Furthermore, the preliminary classification of its group-invariant solutions is investigated. Cited in 11 Documents MSC: 35Q53 KdV equations (Korteweg-de Vries equations) 35A30 Geometric theory, characteristics, transformations in context of PDEs PDF BibTeX XML Cite \textit{M. Nadjafikhah} and \textit{V. Shirvani-Sh}, Math. Probl. Eng. 2011, Article ID 457697, 9 p. (2011; Zbl 1236.35155) Full Text: DOI arXiv References: [1] S. Lie, Theories der Tranformationgruppen, Dritter und Letzter Abschnitt, Teubner, Leipzig, Germany, 1893. [2] P. J. Olver, Applications of Lie Groups to Differential Equations, vol. 107, Springer, New York, NY, USA, 2nd edition, 1993. · Zbl 0785.58003 [3] G. W. Bluman and S. Kumei, Symmetries and Differential Equations, vol. 81, Springer, New York, NY, USA, 1989. · Zbl 0698.35001 [4] G. W. Bluman and J. D. Cole, Similarity Methods for Differential Equations, Springer, New York, NY, USA, 1974. · Zbl 0292.35001 [5] N. A. Kudryashov and D. I. Sinelshchikov, “Nonlinear evolution equation for describing waves in a viscoelastic tube,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 6, pp. 2390-2396, 2011. · Zbl 1221.74044 [6] N. A. Kudryashov and M. V. Demina, “Traveling wave solutions of the generalized nonlinear evolution equations,” Applied Mathematics and Computation, vol. 210, no. 2, pp. 551-557, 2009. · Zbl 1170.35514 [7] Y. C. Fung, Biomechanics: Mechanical Properties of Living Tissues, Springer, New York, NY, USA, 1993. [8] N. A. Kudryashov and I. L. Chernyavskii, “Nonlinear waves in fluid flow through a viscoelastic tube,” Fluid Dynamics, vol. 41, no. 1, pp. 49-62, 2006. · Zbl 1198.76167 [9] C. G. Caro, T. J. Pedly, R. C. Schroter, and W. A. Seed, The Mechanics of the Circulation, Oxford University Press, Oxford, UK, 1978. · Zbl 1234.93001 [10] M. Nadjafikhah, “Lie symmetries of inviscid Burgers’ equation,” Advances in Applied Clifford Algebras, vol. 19, no. 1, pp. 101-112, 2009. · Zbl 1173.35699 [11] S. V. Khabirov, “Classification of three-dimensional Lie algebras in R3 and their second-order differential invariants,” Lobachevskii Journal of Mathematics, vol. 31, no. 2, pp. 152-156, 2010. · Zbl 1267.17023 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.