| With the development of science,it is found that the governing equations of many problems in physics,mechanics and many other disciplines are nonlinear equation.So the research work of solving nonlinear equations shows very important theoretical sig-nificance and application value.Therefore,solving nonlinear differential equations has become a hot topic in the field of applied mathematics.Hirota bilinear derivative method and generalized bilinear method are effective tools for solving nonlinear differ-ential equations.Based on Hirota bilinear derivative method and generalized bilinear method,we have discussed the lump solutions,interaction phenomena and breather-wave solutions of several nonlinear differential equations in this thesis.The specific research contents are as follows:In chapter 1,the theoretical knowledge required in this paper is briefly summa-rized,such as the development history and present situation of Hirota bilinear deriva-tive method and generalized bilinear method.As well as the development present situation of lump solution,interaction solution and breather-wave solution are intro-duced.In chapter 2,the Sawada-Kotera-Kadomtsev-Petviashvili equation is studied based on Hirota bilinear derivative method.And its lump solutions are obtained with the help of Mathematica.In chapter 3,the Shallow-Water-Wave equation and(3+1)dimensional Boiti-Leon-Manna-Pempinelli equation is studied based on the generalized bilinear method.A generalized Shallow-Water-Wave-like equation corresponding to p=3 is constructed,nineteen kinds of interaction solutions and five breather-wave solutions of this equa-tion are given respectively.A generalized Boiti-Leon-Manna-Pempinelli-like equation corresponding to p=3 is constructed,its lump solutions,lump-soliton solutions and breather-wave solutions are obtained.In chapter 4,the summary and outlook of the research contents of this paper are given,display the possible research contents in the future. |
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