Painleve Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Wronskian and Grammian Form  

作　　者：MENG Xiang-Hua TIAN Bo FENG Qian YAO Zhen-Zhi GAO Yi-Tian 

机构地区：[1]School of Science, P.O. Box 122, Beijing University of Posts and Telecommunications, Beijing 100876, China [2]State Key Laboratory of Software Development Environment, Beijing University of Aeronautics and Astronautics, Beijing 100191, China [3]Key Laboratory of Information Photonics and Optical Communications, Ministry of Education, Beijing University of Posts and Telecommunications, Beijing 100876, China [4]Ministry-of-Education Key Laboratory of Fluid Mechanics and National Laboratory for Computational Fluid Dynamics, Beijing University of Aeronautics and Astronautics, Beijing 100191, China

出　　处：《Communications in Theoretical Physics》2009年第6期1062-1068,共7页理论物理通讯（英文版）

基　　金：Supported by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20060006024 and 20080013006;Chinese Ministry of Education, by the National Natural Science Foundation of China under Grant No. 60772023;by the Open Fund of the State Key Laboratory of Software Development Environment under Grant No. SKLSDE-07-001;Beijing University of Aeronautics and Astronautics;by the National Basic Research Program of China (973 Program) under Grant No. 2005CB321901

摘　　要：In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.

关 键 词：（3＋1）-dimensional variable-coefficient Kadomtsev-Petviashvili equation Painlev@ analysis bilinear form Wronskian determinant Grammian determinant symbolic computation 

分 类 号：O175.24[理学—数学] O175.29[理学—基础数学]