Lump solutions to dimensionally reduced Kadomtsev–Petviashvili-like equations

详细信息    查看全文

• 作者：Jian-Ping Yu ; Yong-Li Sun
• 关键词：Lump solutions ; Generalized bilinear equation ; (3+1) ; dimensional KP ; like equation
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：87
• 期：2
• 页码：1405-1412
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

In this paper, we present a new (3+1)-dimensional KP-like nonlinear partial differential equation and construct the lump solutions, rationally localized in all directions in the space, to its two dimensionally reduced cases. The proposed method in this work is based on a generalized bilinear differential equation, which implies that we can build the lump solutions to the presented KP-like equation from special polynomial solutions to the aforementioned generalized bilinear equation. Since there are totally six free parameters in the resulting lump solutions, we can get the sufficient and necessary conditions guaranteeing analyticity and rational localization of the solutions by using these six free parameters. Two special cases are plotted as illustrative examples, and some contour plots with different determinant values are presented to show that the corresponding lump solution tends to zero when the determinant approaches zero.