  In this paper, the nonlinear Gardner-Kawahara (NLGK) equation has been
investigated by using the Lie symmetry method. The symmetry method is applied
to derive the infinitesimal generators and vector fields. The Lie symmetry
method has reduced the nonlinear Gardner-Kawahara equation into a nonlinear
ordinary differential equation form. In this article, we have obtained the
exact solution of the NLGK equation in the explicit form by different
significant methods. Further, the multiplier method has been used to derive the
conservation laws of the nonlinear Gardner-Kawahara equation.
