Bi-directional solitons of dual-mode Gardner equation derived from ideal fluid model

Abstract

In this article, the main goal is to find the exact solution to the dual-mode Gardner equation derived from the ideal fluid model. To achieve this, two distinct methods will be employed: the tan/cot method and the tanh/coth method. Using these methods, the problem can be seen through different angles, providing a full understanding of how the equation works and the various solutions it provides. Furthermore, the periodic, kink and singular solutions will be illustrated through the use of 3D and 2D graphs. This visualization will clearly show how the phase velocity parameter affects the solutions, improving our understanding of wave dynamics within the dual-mode Gardner equation. The findings from this study help in understanding how both solitons and periodic solutions influence wave behavior in shallow water and how light travels through optical fibers.