Research On The Soliton Solutions Of The Space-time Fractional Burgers Equations

The symbolic computing system plays an important role in solving the exact solutions of fractional-order nonlinear partial differential equations.With the help of this Maple symbolic computation to streamline fractional nonlinear partial differential equations large differential and algebraic operations are completed their exact solutions solving the three-dimensional image corresponding to the draw.Maple built a wealth of mathematical symbols computational tools and graphics evolution drawing tools.Draw the exact solution of the image can be more intuitive help us to analyze nonlinear models,to better understand its nature.With the in-depth study of natural phenomena,ordinary nonlinear models can not meet the research needs,so fractional calculus and fractional nonlinear partial differential equations have been widely used.This paper introduces three common definitions of fractional calculus:the Caputo definition,the Grunwald-Letnikov definition,the Riemann-Liouville definition,and the Jumarie modified Riemann-Liouville fractional derivative definition that combines the advantages of the above definitions.In this paper,we use the fractional complex transformation provided by Li and He to transform the fractional nonlinear partial differential equation into an integer order partial differential equation by means of Gamma function and Jumarie's modified Riemann-Liouville fractional derivative definition.Therefore,many methods for solving constant-order ordinary differential equations can be applied to fractional-order partial differential equations.For example,Backlund transformation method,Riccati equation method,homogeneous balance method,exponential function method,auxiliary equation method and so on.In this paper,we use two of the most commonly used classical equations in the cluster of time-space fractional Burgers equations:the space-time fractional Burgers equation and the space-time fractional Sharma-Tasso-Olver equation.The exp-function expansion of the extended negative exponential power is studied.The application of the method and(G'/G,1/G)-expansion method to solve the exact solution of fractional nonlinear partial differential equations.The single-wave solutions,hyperbolic function solutions,trigonometric function solutions and rational function solutions of the space-time fractional Burgers equation and the space-time fractional Sharma-Tasso-Olver equation are obtained.By several traveling wave solutions in the assignment parameters obtained M-type,period,single knot type knot trans type,kink singular type,like dark soliton type of special three-dimensional view more solitary wave.Finally,the two kinds of solving methods used herein were compared with other methods to solve,analyze their strengths and weaknesses.