摘要
在这篇论文，我们为一个可变系数的 Kadomtsev 打 Petviashvili 的方程导出双线性的形式。基于双线性的形式，我们获得 Wronskian 决定因素答案，它确实被证明是通过 Wronskian 技术的这个方程的一个准确答案。另外，我们证明那这个方程能被借助于 Pfaffian 衍生物公式把它的答案看作一个 Grammian 决定因素归结为 Jacobi 身份。
In this paper, we derive the bilinear form for a variable-coefficient Kadomtsev Petviashvili-typed equation. Based on the bilinear form, we obtain the Wronskian determinant solution, which is proved to be indeed an exact solution of this equation through the Wronskian technique. In addition, we testify that this equation can be reduced to a Jacobi identity by considering its solution as a Grammian determinant by means of Pfaffian derivative formulae.
基金
The project supported by the Key Project of the Ministry of Education under Grant No.106033
the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.20060006024
National Natural Science Foundation of China under Grant Nos.60372095 and 60772023
the Open Fund of the State Key Laboratory of Software Development Environment under Grant No.SKLSDE07-001
Beijing University of Aeronautics and Astronautics,and the National Basic Research Program of China(973 Program)under Grant No.2005CB321901
