Special Methods For Exact Solutions Of Several Kinds Of Partial Differential Equations

Duan XiaofangComputational MathematicsDirected by Lu JunliangMany phenomena in natural sciences can be described by partial differential equa-tions.With the rapid development of various fields and the application of partial dif-ferential equations in various fields,many scholars want to solve the exact solutions of partial differential equations to study its application mechanism which lied a solid foundation for research in all directions.Due to the wide application of partial differential equations,more and more schol-ars are studying partial differential equations.At present,many scholars have proposed many methods to solve the exact solutions of partial differential equations.However,due to the nonlinear complexity of partial differential equations,there is no universal method to find their exact solutions.Therefore,it is still very important and valuable to find a method to solve the exact solutions of partial differential equations.Our task is to find different new methods to solve the exact solutions of partial differential equations.The work of this paper is as follows:The first part is mainly to give a brief introduction to nonlinear partial differ-ential equations,a brief introduction to the traveling wave solutions of mathematical and physical equations,some methods for solving exact solutions of partial differential equations,and an introduction to the structure of the paper.The second part introduces the modified hyperbolic function expansion method and its application,which is divided into four parts.These four parts respectively intro-duce the algorithm of the modified hyperbolic function expansion method,the hyper-bolic function solution,the use of the modified hyperbolic function expansion method to obtain the exact solution of the Boiti-Leon-Manna-Pempinelli(BLMP)equation and the Benjamin-Bona- Exact solutions of Mahony(BBM)equation.The third part introduces the modified Riccati auxiliary equation method,which is divided into three parts.These three parts respectively introduce the algorithm of the modified Riccati equation method,the Riccati equation solution and the exact solution of the Kd V- Burgers-Kuramoto equation obtained by the modified Riccati auxiliary equation method.