Symmetries,optimal system,exact and soliton solutions of(3+1)-dimensional Gardner-KP equation  

作　　者：Amjad Hussain Ashreen Anjum M.Junaid-U-Rehman Ilyas Khan Mariam A.Sameh Amnah S.Al-Johani 

机构地区：[1]Department of Mathematics,Quaid-I-Azam University 45320,Islamabad 44000,Pakistan [2]Department of Mathematics,College of Science Al-Zulfi,Majmaah University,Al-Majmaah,P.O Box 66,Majmaah 11952,Saudi Arabia [3]Electrical Engineering Department,Faculty of Engineering and Technology,Future University in Egypt,New Cairo 11845,Egypt [4]Mathematics Department,Faculty of Science,University of Tabuk,Tabuk,Saudi Arabia

出　　处：《Journal of Ocean Engineering and Science》2024年第2期178-190,共13页海洋工程与科学（英文）

基　　金：The authors would like to thank the Deanship of Scientific Research at Majmaah University for supporting this work under Project R-2022-178.

摘　　要：In this research article,the(3+1)-dimensional nonlinear Gardner-Kadomtsov-Petviashvili(Gardner-KP)equation which depicts the nonlinear modulation of periodic waves,is analyzed through the Lie group-theoretic technique.Considering the Lie invariance condition,we find the symmetry generators.The pro-posed model yields eight-dimensional Lie algebra.Moreover,an optimal system of sub-algebras is com-puted,and similarity reductions are made.The considered nonlinear partial differential equation is re-duced into ordinary differential equations(ODEs)by utilizing the similarity transformation method(STM),which has the benefit of yielding a large number of accurate traveling wave solutions.These ODEs are further solved to get closed-form solutions of the Gardner-KP equation in some cases,while in other cases,we use the new auxiliary equation method to get its soliton solutions.The evolution profiles of the obtained solutions are examined graphically under the appropriate selection of arbitrary parameters.

关 键 词：Gardner-KP equation Lie symmetry analysis Optimal system New auxiliary equation method Solitary wave solutions 

分 类 号：O17[理学—数学]