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.

本文通过李对称分析，构造了两个孤子解的相互作用，扭结与其他类型的帕夫洛夫方程孤波解的相互作用。计算基于帕夫洛夫方程的一维子代数的最优系统，并将其用于确定一组不变解。此外，借助李群方法，将Pavlov方程简化为变量数较少的新微分方程，以便进行解析求解。这项研究为我们提供了十四种通用和特殊形式的精确解决方案。通过选择在新的不变解中获得的任意函数，我们构造了物理上有意义的解，并用图形说明了它们。此外，通过调用乘数法可以获得Pavlov方程的守恒律。