The Weierstrass Elliptic Function Solutions And Its Degenerate Solutions Of Nonlinear Evolution Equation

There are all kinds of nonlinear wave phenomenon that are often attributed to nonlinear evolution equations to reveal the essence of nonlinear phenomena in nature.It has been widely used in many fields,such as fluid mechanics,solid physics,meteorology and maritime engineering.This paper focuses on Gardner equation,Whitham-Broer-Ka-up equations,(2+1)-dimensional Kadomtsev-Petviashvil equation and(3+1)-dimensional Jimbo-Miwa equation with variable coefficients in nonlinear evolution equations.Through the Weierstrass elliptic function method,the Weierstrass F-expansion method,the Symbolic calculation method of fractional polynomial,Unified representation of Weierstrass elliptic function of traveling wave solutions,Higher-order strange wave solution are obtained of the above four equations and so on.The first chapter is the preface,which mainly introduces the research background and main research methods of the article.In the second chapter,the Weierstrass elliptic function solutions of Gardner equation and Whitham-Broer-Kaup equations is constructed by using the Weierstrass elliptic function solutions of the general elliptic equation.Then,by determining the transformation formula of Weierstrass elliptic function and Jacobi elliptic function,Weierstrass elliptic function solutions can be transformed into Jacobi elliptic function solutions and hyperbolic function solutions.In the third chapter,The Weierstrass elliptic function solutions of the(2+1)-dimensional Kadomtsev-Petviashvil(KP)equation are obtained by using the Weierstrass F-expansion method.With the aid of the conversion formula between Weierstrass elliptic function and Jacobi elliptic function,the solutions of Weierstrass elliptic function are transformed into Jacobi elliptic function solutions.When the elliptic modulus approaches to 0 or 1,Jacobi elliptic function solutions are degenerated into trigonometric func-tion solutions or hyperbolic function solutions.In the forth chapter,on the basis of the Hirota bilinear method.On the one hand,the symbolic calculation method of fractional polynomial is applied.So higher-order rogue wave solutions of the(3+1)-dimensional variable coefficient Jimbo-Miwa equation are obtained.On the other hand,with the help of the homoclinic test method.The abundant mixed wave solutions of the(3+1)-dimensional variable coefficient Jimbo-Miwa equation can be constructed.