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Invariant analysis, optimal system of Lie sub-algebra and conservation laws of (3+1)-dimensional KdV–BBM equation

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Abstract

In this paper, a nonlinear fourth-order (3+1)-dimensional KdV Benjamin–Bona–Mahony equation is studied using Lie symmetry approach. Lie symmetry analysis is executed to obtain the entire vector field, group-invariant solutions and similarity reductions based on the one-dimensional optimal sub-algebra. One-dimensional optimal systems are constructed using adjoint representation of a Lie group on its Lie algebra. Finally, the conservation laws have been obtained by considering the “new conservation theorem” proposed by Ibragimov.

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Acknowledgements

This research work was funded by SERB, Government of India vide Grant Ref. No. CRG/2018/000725. The authors of this manuscript would like to take this opportunity to express their deepest sense of gratitude and thanks to the anonymous reviewer for his fruitful comments and suggestions for the betterment and improvement of the manuscript.

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  1. Department of Mathematics, National Institute of Technology, Rourkela, 769008, India

    Vinita & S. Saha Ray

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  1. Vinita
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  2. S. Saha Ray
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Correspondence to S. Saha Ray.

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Vinita, Saha Ray, S. Invariant analysis, optimal system of Lie sub-algebra and conservation laws of (3+1)-dimensional KdV–BBM equation. Eur. Phys. J. Plus 135, 913 (2020). https://doi.org/10.1140/epjp/s13360-020-00936-1

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  • DOI: https://doi.org/10.1140/epjp/s13360-020-00936-1

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