The Application Of The Hirota Method In Solving Soliton Equations

Content: This dissertation has mainly done the following four as-pects research: First, The Hirota bilinear method is discussed and thebrief application of it is introduced ; Then, the Wronskian techniqueis introduced to the (2+1) dimensional KdV equation and the Wron-skian solutions and the Grammian solutions of the soliton equationare generated; Based on the Jacobi identity, a kind of method of gen-erating Lie algebra is obtained by taking advantage of a low dimensionLie algebra; In the end, by applying the Pfa?anization procedure tothe (2+1) dimensional KdV equation,a new integrable system withPfa?an solutions is generated.The structure of this paper is as follows:Chapter 1 is concerned with the exposition of the development andthe research situation of several subjects which will be discussed inthis paper. The main results of this dissertation are brie?y introducedin this chapter.Chapter 2 review the bilinear solution and explain the brief appli-cations.Chapter 3, based on the introduction of Wronskian solutions andGrammian solutions, we get the solutions of the (2+1) dimensionalKdV equation and popularize it. A kind of methods of generatingLie algebra is obtained by taking advantage of a low dimension Liealgebra.Chapter 4, Pfa?anization procedure is introduced and appiled tothe (2+1) dimensional KdV equation.