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Journal of Applied Nonlinear Dynamics 13(2) (2024) 323--336 | DOI:10.5890/JAND.2024.06.010

Arindam Ghosh, Sarit Maitra

Department of Mathematics, National Institute of Technology Durgapur, India

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Abstract

This paper is aimed to study the KP-BBM equation, which was proposed by Abdul Majid Wazwaz [Wazwaz. A.M.: Applied Mathematics and Computation, 169 (2005), 700–712.]. To check its integrability Painlev\'e test has been performed. Lie Symmetry analysis has been done and point symmetry generators are obtained. The invariants of the Lie algebra are found and the one dimensional optimal system for subalgebras of the obtained Lie algebra is constructed by using the Hu-Li-Chen algorithm. Three similarity reductions and corresponding exact solutions are derived.~Also Homogeneous balance method, $Tanh$ method are used to find exact solutions. Solitary wave like solutions are obtained and plotted for some suitable values of the parameters involved. The effects of the nonlinear coefficient and dispersion coefficient on the obtained solitary waves are discussed.

Acknowledgments

The authors are grateful to NIT Durgapur, India for their research support.

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