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lump-type solutions of a generalized Kadomtsev–Petviashvili equation in(3+1)-dimensions

Chinese Physics B 2019年第10期28卷 245-252页

作者： Xue-Ping Cheng Wen-Xiu Ma Yun-Qing Yang Physics MathematicsInformation College of Zhejiang Ocean UniversityZhoushan 316004China Key Laboratory of Oceanographic Big Data Mining&Application of Zhejiang Province Zhoushan 316022China Department of Mathematics and Statistics University of South FloridaTampaFL 33620-5700USA Department of Mathematics King Abdulaziz UniversityJeddahSaudi Arabia College of Mathematics and Systems Science Shandong University of Science and TechnologyQingdao 266590China International Institute for Symmetry Analysis and Mathematical Modelling Department of Mathematical SciencesNorth-West UniversityMafikeng CampusPrivate Bag X2046Mmabatho 2735South Africa

Through the Hirota bilinear formulation and the symbolic computation software Maple, we construct lump-type solutions for a generalized(3+1)-dimensional Kadomtsev-Petviashvili(KP) equation in three cases of the coefficients in the equation. Then the sufficient and necessary conditions to guarantee the analyticity of the resulting lump-type solutions(or the positivity of the corresponding quadratic solutions to the associated bilinear equation) are discussed. To illustrate the generality of the obtained solutions, two concrete lump-type solutions are explicitly presented, and to analyze the dynamic behaviors of the solutions specifically, the three-dimensional plots and contour profiles of these two lump-type solutions with particular choices of the involved free parameters are well displayed.

关键词： lump-type solution generalized(3+1)-dimensional Kadomtsev-Petviashvili equation Hirota bilinear form symbolic computation

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High-Order lump-type Solutions and Their Interaction Solutions to a (3+1)-Dimensional Nonlinear Evolution Equation

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Communications in Theoretical Physics 2019年第8期71卷 927-934页

作者： Tao Fang Hui Wang Yun-Hu Wang Wen-Xiu Ma College of Art and Sciences Shanghai Maritime University Shanghai 201306 China Department of Mathematics and Statistics University of South Florida Tampa FL 33620 USA Department of Mathematics and Information Technology The Education University of Hong Kong Hong Kong China Department of Mathematics King Abdulaziz University Jeddah Saudi Arabia College of Mathematics and System Science Shandong University of Science and Technology Qingdao 266590 China Department of Mathematical Sciences North-West University Mafikeng Campus Mmabatho 2735 South Africa

By means of the Hirota bilinear method and symbolic computation, high-order lump-type solutions and a kind of interaction solutions are presented for a(3+1)-dimensional nonlinear evolution *** high-order lumptype solutions of the associated Hirota bilinear equation are presented, which is a kind of positive quartic-quadraticfunction *** the same time, the interaction solutions can also be obtained, which are linear combination solutions of quartic-quadratic-functions and hyperbolic cosine *** properties and dynamical structures of two classes of the presented solutions are demonstrated in detail by their graphs.

关键词： high-order lump-type solutions interaction solutions Hirota bilinear method

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