  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.
