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

Guiming Jin¹ ; Xueping Cheng² ; Jianan Wang¹ ; Hailiang Zhang¹

¹ School of Information Engineering, Zhejiang Ocean University, Zhoushan 316022, PR China
² School of Science, Zhejiang University of Science and Technology, Hangzhou 310023, PR China

Mathematical modelling of natural phenomena, Tome 19 (2024), article no. 9.

Résumé

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.

Détail

DOI : 10.1051/mmnp/2024004

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