Group Analysis and Exact Soliton Solutions to a New (3+1)-Dimensional Generalized Kadomtsev-Petviashvili Equation in Fluid Mechanics
Qin Zhoua, Aimin Pana, Seyed Mehdi Mirhosseini-Alizaminib, Mohammad Mirzazadehc, Wenjun Liud, Anjan Biswase, f
aSchool of Electronics and Information Engineering Wuhan Donghu University, Wuhan 430212, Peoples Republic of China
bDepartment of Mathematics, Payame Noor University (PNU), P.O. Box 19395-3697, Tehran, Iran
cDepartment of Engineering Sciences, Faculty of Technology and Engineering, East of Guilan, University of Guilan, P.C. 44891-63157, Rudsar-Vajargah, Iran
dState Key Laboratory of Information Photonics and Optical Communications and School of Science, P. O. Box 122 Beijing University of Posts and Telecommunications, Beijing 100876, China
eDepartment of Physics, Chemistry and Mathematics, Alabama A&M University, Normal, AL-35762, USA
fDepartment of Mathematics and Statistics, Tshwane University of Technology, Pretoria-0008, South Africa
Received: February 19, 2018; in final form July 9, 2018
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This work studies a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation analytically. This model is a version of the Kadomtsev-Petviashvili equation that addresses shallow water waves in (2+1)-dimensions. Based on the Lie group method, the symmetry reductions and traveling wave reduction are obtained. Finally, explicit solitons including the soliton solutions are constructed by a couple of integration methods, which are the power series approach, subsidiary ordinary differential equation scheme, and the sine-Gordon expansion method.

topics: solitons, group analysis, symmetry analysis, exact solutions