Lie Symmetry Analysis and Some New Exact Solutions to the KP-BBM Equation

Abstract: This paper is aimed to study the KP-BBM equation, which was proposed by Abdul Majid Wazwaz in 2005. To check its integrability Painleve 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.