(2 +1) - Maintenance Is Of Broer-kaup-kupershmidt Equations, Bilinear And Precise Solution

The soliton equation is one of the most prominent subject in the fields of nonliear science. In this paper, we consider a modified Broer-Kaup-Kupershmidt equation. there are sevral systematic approches to obtain solutions of soliton equation. The Hirota's direct method has been proved to be one of the most important method in soliton theory. In the paper ,the modified Broer-Kaup-Kupershmidt equation are transformed into a bilinear differential equation. Some exact solutions for the eqations are obtained by Hirota method.In this thesis .there are four parts. In section one ,we mainly introduce backgrouding knowledge and the essentials of the direct methods in soliton theory.In section two ,we consider the (1+1)-dimension modified Broer-Kaup-Kupershmidt soliton equation. The (1+1)-dimension modified Broer-Kaup-Kupershmidt soliton equation can be transformed into bilinear differential equations through Bi-logarithmic transformation, the Bi-logarithmic transformations are:and the bilinear differential equations are:Some exact soliton solutions are obtained by Hirota method. In section three ,weconsider the (2+1)-dimension modified Broer-Kaup-Kupershmidt soliton equation. The (2+1)-dimension modified Broer-Kaup-Kupershmidt soliton equation can be transformed into bilinear differential equations through Bi-logarithmic transformation. the Bi-logarithmic transformation are:and the bilinear differential equations are:Some exact solutions for the eqations are obtained by Hirota method.