Inverse Scattering Transformation And Exact Solutions Of (2+1)-Dimensional Variable-Coefficient KP Equation

This paper mainly uses the(2+1)-dimensional variable-coefficient KP equation to carry out the research.The inverse scattering transformation method is extended to the derived variablecoefficient equation and use the F-expansion method to obtain some exact solutions of this equation.The advantage of the F-expansion method is one can find some exact solutions of the nonlinear evolution equation,and it can also be used to obtain many new or more general solutions.Chapter 1 discusses the origin of the soliton theory,the historical process of the inverse scattering transformation method,introduces the F-expansion method and explains the main work of this article.Chapter 2 uses the Lax pair to derive a(2+1)-dimensional variable-coefficient KP equation,in which the coefficient functions meet certain constraints.The relationship between the coefficients of this equation can be used to derive the KPI equation and KPII equation,so it can be seen that this equation is general.In Chapter 3,taking the equation introduced in Chapter 2 as a model,the spectral problem and time evolution equation are derived by the Lax pair given in Chapter 2.Then in Chapter 3uses the direct scattering analysis to obtain all the scattering data of the equation,and then obtain the law of the scattering data of the equation over time according to the inverse scattering transformation analysis.Finally,the inverse scattering transformation method is used to find the rogue wave solution of the equation.In Chapter 4,the constraint relationship between the coefficient functions of the derived equation are weaken.At the same time,chapter 4 uses the F-expansion method to obtain some exact solutions of the equation,such as Jacobi elliptic function solutions,hyperbolic function solutions and trigonometric function solutions.