中文摘要：

In this paper, new extended Grammian determinant solutions to a(3 + 1)-dimensional KP equation are presented by using Hirora’s bilinear method, and a broad set of sufficient conditions of systems of linear partial differential equations is given. Moreover, some special solutions of the representative systems are obtained through a systematic analysis.

英文摘要：

In this paper, new extended Grammian determinant solutions to a （3 ＋ 1）-dimensional KP equation are presented by using Hirora＇s bilinear method, and a broad set of suftlcient conditions of systems of linear partial differential equations is given. Moreover, some special solutions of the representative systems are obtained through a systematic analysis.