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Invariant analysis and exact solutions of nonlinear time fractional Sharma–Tasso–Olver equation by Lie group analysis

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Abstract

This paper is concerned with the time fractional Sharma–Tasso–Olver (FSTO) equation, Lie point symmetries of the FSTO equation with the Riemann–Liouville derivatives are considered. By using the Lie group analysis method, the invariance properties of the FSTO equation are investigated. In the sense of point symmetry, the vector fields of the FSTO equation are presented. And then, the symmetry reductions are provided. By making use of the obtained Lie point symmetries, it is shown that this equation can transform into a nonlinear ordinary differential equation of fractional order with the new independent variable ξ=xt −α/3. The derivative is an Erdélyi–Kober derivative depending on a parameter α. At last, by means of the sub-equation method, some exact and explicit solutions to the FSTO equation are given.

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Acknowledgements

The project is supported by the National Natural Science Foundation of China (NNSFC) (Grant No. 11171022). The authors express their sincere thanks to the referees for their careful review this manuscript and their useful suggestions.

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  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, P.R. China

    Gang-Wei Wang & Tian-Zhou Xu

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  1. Gang-Wei Wang
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  2. Tian-Zhou Xu
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Correspondence to Gang-Wei Wang.

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Wang, GW., Xu, TZ. Invariant analysis and exact solutions of nonlinear time fractional Sharma–Tasso–Olver equation by Lie group analysis. Nonlinear Dyn 76, 571–580 (2014). https://doi.org/10.1007/s11071-013-1150-y

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  • DOI: https://doi.org/10.1007/s11071-013-1150-y

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