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On group analysis, conservation laws and exact solutions of time-fractional Kudryashov–Sinelshchikov equation

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Abstract

In this paper, a systematic study for finding the symmetry group classification is performed for the time-fractional Kudryashov–Sinelshchikov equation, which describes the pressure waves in liquid with gas bubbles. Using Lie symmetries, the vector fields, and invariance properties of the underlying equation with various cases are presented and then similarity reductions are obtained. Furthermore, using the new conservation theorem, conservation laws are constructed for all possible cases. Finally, based on the invariant subspace method, a variety of exact solutions are derived using the obtained invariant subspaces, including the trigonometric, exponential, and polynomial type of solutions.

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Acknowledgements

The author wishes to thank the editor and anonymous referees for their helpful comments and suggestions for the significant improvement of the manuscript.

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  1. Department of Mathematics, Amrita School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore, 641112, India

    P. Prakash

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Communicated by Vasily E. Tarasov.

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Prakash, P. On group analysis, conservation laws and exact solutions of time-fractional Kudryashov–Sinelshchikov equation. Comp. Appl. Math. 40, 162 (2021). https://doi.org/10.1007/s40314-021-01550-2

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