This paper mainly studied two types of equations:the variable-coefficient Manakov model and the coupling Schrodinger equation. Based on the Hirota’s bilinear method and Wronskian technique, the Wronskian form solutions is obtained and its progressive analysis between the two solitons are investigated.The first chapter mainly introduces the generation and development of the soliton theory. The second chapter summarizes some related concepts and formulas, such as Hirota operator and Wronskian determinant with their definitions and properties.In chapter three, We mainly recommend the Wronskian solutions of variable-coefficient Manakov model. In the first place, we introduce potential equation transformation that it can be converted into the bilinear form. Then, on the basis of the double linear equation, the Wronskian determinant can be made by introducing some new functions. The ratio-nal solutions are obtained by using the Wronskian technique. As a case of double soliton solution of the collision, its dynamic properties and progressive analysis is discussed.The coupling Schrodinger equation is discussed in chapter four. Because of the practicability of this Wronskian technique, we can take similar way. The Schrodinger equation is three coupling equation, here, we set up new fourth Wronskian determinant to resolve this problem. After substituting into the original equation, the Wronskian is obtained through the restrictive conditions which is necessary, and we give its proof later. |