Abstract
The manuscript considers the dynamical symmetry usage to the integration of ODE. Symmetries with invariants guaranteeing the lowering of the ODE order are suggested. These symmetries include the whole class of point symmetries. The procedure for the dynamical symmetries finding is demonstrated. Concrete examples of the using of dynamical symmetries are given. The manuscript considers the application of the obtained solutions to the investigation of the nonlinear heat conduction equation.
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References
Stephani H (1989) Differential equations: their solution using symmetries. Cambridge University Press, Cambridge
Timoshin MI (2009) Dynamic symmetries of ODEs. Ufim Math J 1(3):132–138
Ibragimov NH (1985) Transformation groups applied to mathematical physics. Reidel, Dordrecht
Ovsjannikov LV (1982) Group analysis of differential equations. Academic, New York
Berkovich LM (1992) Factorization as the method of the finding of exact invariant solutions for Kolmogorov-Petrovsky-Piskunov equation and connected with it Semyonov and Zeldovich equation. DAN 322(5):823–827
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© 2012 Springer Science+Business Media, LLC
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Timoshin, M.I. (2012). Dynamical Symmetries of Second Order ODE. In: Luo, A., Machado, J., Baleanu, D. (eds) Dynamical Systems and Methods. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0454-5_9
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DOI: https://doi.org/10.1007/978-1-4614-0454-5_9
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Online ISBN: 978-1-4614-0454-5
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