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《中国物理B》 2019-10
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Lump-type solutions of a generalized Kadomtsev–Petviashvili equation in(3+1)-dimensions

Xue-Ping Cheng;Wen-Xiu Ma;Yun-Qing Yang;Physics, Mathematics, and Information College of Zhejiang Ocean University;Key Laboratory of Oceanographic Big Data Mining & Application of Zhejiang Province;Department of Mathematics and Statistics, University of South Florida;Department of Mathematics, King Abdulaziz University;College of Mathematics and Systems Science, Shandong University of Science and Technology;International Institute for Symmetry Analysis and Mathematical Modelling, Department of Mathematical Sciences, North-West University;  
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.
【Fund】: Project supported by the National Natural Science Foundation of China(Grant Nos.11505154 11605156 11775146 and 11975204);; the Zhejiang Provincial Natural Science Foundation of China(Grant Nos.LQ16A010003 and LY19A050003);; the China Scholarship Council(Grant No.201708330479);; the Foundation for Doctoral Program of Zhejiang Ocean University(Grant No.Q1511);; the Natural Science Foundation(Grant No.DMS-1664561);; the Distinguished Professorships by Shanghai University of Electric Power(China);; North-West University(South Africa);; King Abdulaziz University(Saudi Arabia)
【CateGory Index】: O175
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