The Exact Solutions Of (2+1)-Dimension Boussinesq-Burgers Equation

In this paper, we consider an important soliton equation. We catch the exact soliton solutions by the direct method. There are three sections in this thesis.In section one.we mainly introduce the backgrouding knowledge about the the soliton theory and the essentials of the direct method.In section two, through the proper transformation,the soliton equation can be transformed into bilinear differential equations. For the (2+1)-dimension soliton equation,it is difficult to find the proper transformation.We introduce the Bi-Logarithm transformation:u=—(1/2)(ln(g/f))_x,,v = -(1/2)(ln gf)_xx the equationcan be transformed into the bilinear differential equations,as followsAttacca,we obtained the exact N-Soliton solutions by the perturbation method,and the solutionsare the following:moreover,We plot the beautiful single-double soliton collision figures by matlab,and watch the phenomenon of soliton wave directly.In the last section, the method to find the exact N-Soliton solutions of the (1+1)-dimension Boussinesq-Burgers soliton equation is similar with the (2+1)-dimension, we don't discuss agian. We mainly catch the another type solution-Wronskian solution of the (1+1)-dimension Boussinesq-Burgers soliton equation from the bilinear differential equations.The key of the method is to find a appropriate determinants elementφ.In the thesis ,we find the appropriate determinants elementsφ,ψfrom the lax pair of the equal spectral problem.more we constuct the appropriate determinants solutions of the soliton equation.