Rational solutions and lump solutions to the generalized -dimensional Shallow Water-like equation

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• 作者：Yong Zhang ; Huanhe Dong ; ^{mathsdong@126.com} ; Xiaoen Zhang ; Hongwei Yang
• 关键词：Generalized bilinear derivative ; (3+1)(3+1)-dimensional Shallow Water-like equation ; Rational solution ; Lump solution
• 刊名：Computers & Mathematics with Applications
• 出版年：2017
• 出版时间：15 January 2017
• 年：2017
• 卷：73
• 期：2
• 页码：246-252
• 全文大小：775 K
• 卷排序：73

文摘

Through symbolic computation with Maple, the rational solutions and the lump solutions of the generalized (3+1)(3+1)-dimensional Shallow Water-like equation are presented by using the generalized bilinear operator when the parameter p=3p=3. It is pointed that these rational solutions are classified into five classes because they are obtained mainly by depending on the polynomial solutions. The resulting lump solutions which are rationally localized in all directions in the space are acquired by making use of the quadratic function. However, not every nonlinear partial differential equation has the lump solutions, if any, the quantity of the lump solutions is fewer than the rational solutions. Only one class of lump solutions of the generalized (3+1)(3+1)-dimensional Shallow Water-like equation is gotten and three 3D plots with specific values of the involved parameters are plotted.