摘要
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.
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.
作者
Xue-Ping Cheng
Wen-Xiu Ma
Yun-Qing Yang
程雪苹;马文秀;杨云青(Physics,Mathematics,Information College of Zhejiang Ocean University,Zhoushan 316004,China;Key Laboratory of Oceanographic Big Data Mining&Application of Zhejiang Province,Zhoushan 316022,China;Department of Mathematics and Statistics,University of South Florida,Tampa,FL 33620-5700,USA;Department of Mathematics,King Abdulaziz University,Jeddah,Saudi Arabia;College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao 266590,China;International Institute for Symmetry Analysis and Mathematical Modelling,Department of Mathematical Sciences,North-West University,Mafikeng Campus,Private Bag X2046,Mmabatho 2735,South Africa)
基金
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)
