Study On Conservation Law And Exact Solution Of Two Kinds Of(2+1) Dimensional BBM Type Equations

The(2+1)-dimensional KP-BBM equation and(2+1)-dimensional BBM equation play an important role in the field of physics and mechanics.Among them,the(2+1)-dimensional KP-BBM equation reflects the long-wave single-term propagation model in fluid,and the(2+1)-dimensional BBM equation mainly describes the one-way propagation model of long wave in some nonlinear scattering system.In this thesis,classical Lie symmetry analysis method and double reduction method are used to study the exact solutions and conservation laws of two kinds of(2+1)dimensional nonlinear equations.The main research contents and achievements are as follows:The first part of this thesis deals with the Lie Symmetry,Conservation Law,Reduction and Exact Solutions of Equations of the special generalized(2+1)dimensional Kadomtsov-Petviashivilli-Benjamin-Bona-Mahony(KP-BBM)equation.According to Lie symmetry analysis,five infinitesimal generators are obtained and the conservative forms of two generators satisfying the conservation law conditions are calculated.By using the double reduction theory,the generalized KP-BBM equation is reduced to two forms of ordinary differential equations.Finally,the exact solutions of the original equation are obtained by solving these ordinary differential equations,and by choosing appropriate parameters,the images of these solutions are given.In the second part of this paper,Lie symmetry,conservation law,double reduction and exact solution of Benjamin-Bona-Mahony(BBM)equation are studied,and two conservation laws of BBM equation can be obtained by using multiplier method.Next,the partial differential BBM equation is reduced to ordinary differential equation by using the generalized double reduction theory.Then we use the Sine-Cosine method to find the new exact solutions of the reduced ordinary differential equation and present some of its imagesThe study of these two kinds of(2+1)dimensional BBM-type equations is helpful to better understand the trajectory of the hydrodynamic model.