Application Of (G'/G)-Expansion Method And F-expansion Method Of Solution To Nonlinear Evolution Equations

The study of non-linear science is one of the mainstreams in the development and research of science and technology in the 21st century.It focuses on the most basic mathematical theories and methods in the movement of objects,sound transmission and various laws of change in nature.Principles and laws in many fields,such as physics,chemistry,biology,finance and engineering,can be described by appropriate partial differential equations.From the development of non-linear science,we can see that the non-linear evolution equation is closely related to many disciplines,such as Maxwell equation in electromagnetics,continuity equation in fluid mechanics,weather prediction equation in atmospheric dynamics,and some theoretical problems in the utilization of water resources,etc.The study of non-linear evolution equation provides an effective way to solve these practical problems.In the process of studying partial differential equation,people constantly put forward new ideas and methods,which greatly enrich the content of partial differential equation and promote the development of related disciplines.Nonlinear science,especially the theory of non-linear partial differential,is an important research direction in modern science.When it is connected with some practical problems and natural phenomena,it is generally necessary to establish nonlinearity.The model is implemented,and the non-linear partial differential equation is one of the more accurate models to describe the non-linear phenomena.From the traditional point of view,it is very difficult to find the analytical solution-also known as exact solution-of partial differential equation.However,after years of exploration and research,people have found some methods to construct analytic solutions for a series of nonlinear partial differential equations.This kind of equation is usually used to describe the evolution process of various phenomena over time.We call it a non-linear evolution equation or evolution equation.In the history of the development of non-linear science,people have gradually made progress in the field of non-linear science,and accumulated many methods to solve the exact solutions of non-linear evolution equations.For example,the well-known backscattering method,auxiliary equation method,extended hyperbolic tangent function method,expansion method,F expansion method,homogeneous balance method,Backlund transformation method,hyperbolic function expansion method,first integration method,similarity reduction method,Darbouxb transformation method and various function transformation methods are all effective methods to construct analytical solutions of some nonlinear evolution equations.Many exact solutions of the nonlinear evolution equation obtained by these methods reasonably explain the related natural phenomena and greatly promote the development of related disciplines such as physics,mechanics,Applied Mathematics and engineering technology.In this paper,we will start with the expansion method and F-expansion method to solve(2+1)dimensional coupled nonlinear sytem of Schrodinger equations(?) and(2+1)dimensional BLMP equation (?),compare them with the exact solutions obtained by other literature methods,so as to enrich the solution systems of non-linear Schrodinger equation and BLMP equation.