Symmetry Analysis Of Several Nonlinear Evolution Equations Based On Symbolic Compution

In recent decades,the nonlinear evolution equations have penetrated into the fields of physics,chemistry,machinery and so on,and become the focus and hot topic of scholars'research.Using the nonlinear evolution equations to model the practical problems of natural phenomena and engineering technology helps us to better understand the essence and law of the development of things.With the development of scientific research,many methods have been explored to solve the nonlinear evolution equations.However,there is no unified method to solve the nonlinear evolution equations so far.Based on the Lie symmetry analysis method,this paper studies the exact solutions of three nonlinear evolution equations by combining the power series method and tanh method.The specific contents are as follows:(i)We utilize the Lie symmetry analysis method and the power series method to solve the coupled integrable dispersionless equations.First,we use Lie symmetry analysis method to obtain the similarity reduction equations and the group invariant solutions.Moreover,we derive their approximate analytical solutions by the method of power series.Finally,using lbragimov's method,we set up the conservation laws.(ii)The(3+1)-dimensional BKP-Boussinesq equation is solved by the Lie symmetry analysis and tanh method.Firstly,the corresponding reduced equations are given by using Lie symmetry analysis method.Secondly,its exact solutions are obtained by the tanh method.Finally,the conservation laws are constructed by lbragimov's method.(iii)We use Lie symmetry analysis method and tanh method to solve the(3+1)dimensional nonlinear wave equation.Firstly,the optimal system of one-dimensional subalgebras is derived by Lie symmetry analysis method and the reduced equations are obtained.Secondly,we obtain the exact solutions by the tanh method.