In this paper, based on Hirota＇s bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial ...In this paper, based on Hirota＇s bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented. They guarantee that the Wronskian determinant and the Grammian determinant solve the （3 ＋ 1）-dimensional Jimbo-Miwa equation in the bilinear form. Then some special exact Wronskian and Grammian solutions are obtained by solving the differential conditions. At last, with the aid of Maple, some of these special exact solutions are shown graphically.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11202161 and 11172233)the Basic Research Fund of the Northwestern Polytechnical University,China(Grant No.GBKY1034)
文摘In this paper, based on Hirota＇s bilinear method, the Wronskian and Grammian techniques, as well as several properties of the determinant, a broad set of sufficient conditions consisting of systems of linear partial differential equations are presented. They guarantee that the Wronskian determinant and the Grammian determinant solve the （3 ＋ 1）-dimensional Jimbo-Miwa equation in the bilinear form. Then some special exact Wronskian and Grammian solutions are obtained by solving the differential conditions. At last, with the aid of Maple, some of these special exact solutions are shown graphically.
