Solutions and conservation laws of Benjamin-Bona-Mahony-Peregrine equation with power-law and dual power-law nonlinearities

In this paper, exact solutions of Benjamin-Bona-Mahony-Peregrine equation are obtained with power-law and dual power-law nonlinearities. The Lie group analysis as well as the simplest equation method are used to carry out the integration of these equations. The solutions obtained are cnoidal waves, periodic solutions and soliton solutions. Subsequently, the conservation laws are derived for the underlying equations.