Dynamics and Exact Solutions of Third-order Nonlinear Evolutionary Differential Equations

This article proposes an approach to constructing exact solutions of a third-order nonlinear evolutionary differential equation based on the theory of finite-dimensional dynamics. This theory, in turn, is based on the theory of shuffling symmetries of ordinary differential equations and it is a natural extension of the theory of dynamical systems to evolutionary partial differential equations. theory of finite-dimensional dynamics makes it possible to find families of solutions of evolution equations, depending on a finite number of parameters, among all solutions of such equations.