Interaction Solutions Of Some Nonlinear Partial Diferential Equations Gao Meiru

The soliton theory is an important branch of nonlinear science. Finding ex-plicit and exact solutions of nonlinear partial diferential equations(PDEs) plays animportant role in soliton theory. Nowadays, with the availability of computer sym-bolic systems such as MAPLE and MATHEMATICA,which allow us to performsome complicated and tedious algebraic calculations on computers, many new exactattractive solutions of PDEs have been found.Single periodic soliton solutions, or multiple soliton solutions and mixed solu-tion between single periodic solutions have been mostly seeked. However, few peoplesearch interactions between single periodic solitons and doubly periodic solutions orinteractions between doubly periodic solutions. Although the single-cycle solitonsolution is a limiting case of doubly periodic solutions, seeking such interactions isvery difcult.The dissertation introduces Jacobi elliptic function expansion method. Thenbased on an improved auxiliary equation, the existing results are enriched and de-veloped. Taking the Boussinesq equation as an example, many interaction solutionsof the same type are obtained. Subsequently, based on the Hirota bilinear methodand the Wronskian techniques, interaction solutions of diferent type functions tosome nonlinear partial diferential equations are given. The basic content of thispaper is arranged as follows:The first chapter briefly introduces nonlinear partial diferential equations andtheir exact solutions, especially expounds the background and the development ofsoliton theory, and finally illustrates the topic and the main work in this paper.The second chapter describes three common methods for seeking exact solutionsof nonlinear partial diferential equations. They are the Jacobi elliptic functionexpansion method, Hirota bilinear method, and the Wronskian techniques.In chapter III, the traditional Jacobi elliptic function method is improved,and the existing conclusions are enriched and developed. Taking the Boussinesqequation as an example, some interactions between the same type functions areobtained. Then, through the Wronskian form expansion method, new interactions between diferent type functions to several nonlinear partial diferential equationsare obtained.