Lie Symmetry Analysis, Optimal System, New Solitary Wave Solutions and Conservation Laws of the Pavlov Equation

In this paper, an interaction of two-soliton solutions, interactions of the kink with other types of solitary wave solutions of Pavlov equation are constructed via Lie symmetry analysis. The optimal system based on one-dimensional subalgebras of Pavlov equation is computed and used to determine a group of invariant solutions. Furthermore, the Pavlov equation is reduced, with the help of Lie group method, to new differential equations with less number of variables in order to solve it analytically. This study leads us to fourteen exact solutions in general and special forms. Through an ansätz in the choice of the arbitrary functions obtained in the new invariant solutions, we construct physically meaningful solutions and illustrate them graphically. Moreover, conservation laws are obtained for the Pavlov equation by invoking the multiplier method.