(3+1)-Dimensional Gardner Equation Deformed from (1+1)-Dimensional Gardner Equation and its Conservation Laws

作     者：Jin, Guiming Cheng, Xueping Wang, Jianan Zhang, Hailiang 

作者机构：Zhejiang Ocean Univ Sch Informat Engn Zhoushan 316022 Peoples R China Zhejiang Univ Sci & Technol Sch Sci Hangzhou 310023 Peoples R China 

出 版 物：《MATHEMATICAL MODELLING OF NATURAL PHENOMENA》 (Math. Model. Nat. Phenom.)

年 卷 期：2024年第19卷

核心收录：

学科分类：0710[理学-生物学] 0701[理学-数学] 

基　　金：Training Program for Leading Talents in Universities of Zhejiang Province Scientific Research Foundation of Zhejiang University of Science and Technology National Natural Science Foundation of China, NSFC, (11975204, 12075208) National Natural Science Foundation of China, NSFC 

主　　题：(3+1)-dimensional Gardner equation deformation algorithm Lax pair traveling wave solution symmetry reduction 

摘      要：Through the application of the deformation algorithm, a novel (3+1)-dimensional Gardner equation and its associated Lax pair are derived from the (1+1)-dimensional Gardner equation and its conservation laws. As soon as the (3+1)-dimensional Gardner equation is set to be y or z independent, the Gardner equations in (2+1)-dimension are also obtained. To seek the exact solutions for these higher dimensional equations, the traveling wave method and the symmetry theory are introduced. Hence, the implicit expressions of traveling wave solutions to the (3+1)-dimensional and (2+1)-dimensional Gardner equations, the Lie point symmetry and the group invariant solutions to the (3+1)-dimensional Gardner equation are well investigated. In particular, after selecting some specific parameters, both the traveling wave solutions and the symmetry reduction solutions of hyperbolic function form are given.