Applications Of Algebraic Dynamics Algorithm In Solving Approximate Solutions Of Some Partial Differential Evolution Equations

Algebraic dynamical algorithm is an effective method proposed by Shun-Jin Wang to solve the nonlinear evolution equations by direct expanding solutions in terms of the power series of the infinitesimal time translation operator. However, there are many delta functions in computations so that the corresponding computation becomes complicated. Cheng-shi Liu gives an equivalent construction of the infinitesimal time translation operator including only partial derivative operations, so this construction is very simple for applications.By an equivalent form of the infinitesimal time translation operator in algebraic dynamical algorithm, we apply algebraic dynamical method to solve the high order approximate analytic solutions to some important nonlinear evolution equations such as KdV-Burgers equation, modified Boussinnesq equation, and Pochharmer-Chree equation,nonlinear Schrodinger-like equation and Sinh-Gordon equation. These applications and results are new.