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

doi:10.1088/1674-1056/ab3f20

Abstract 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.

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

Received: 09 April 2019
Revised: 07 August 2019
Accepted manuscript online:

PACS:	02.30.Jr	(Partial differential equations)
	02.70.Wz	(Symbolic computation (computer algebra))
	02.60.Cb	(Numerical simulation; solution of equations)

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), and King Abdulaziz University (Saudi Arabia).

Corresponding Authors: Xue-Ping Cheng
E-mail: chengxp2005@126.com

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Xue-Ping Cheng(程雪苹), Wen-Xiu Ma(马文秀), Yun-Qing Yang(杨云青) Lump-type solutions of a generalized Kadomtsev-Petviashvili equation in (3+1)-dimensions 2019 Chin. Phys. B 28 100203

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

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