Traveling wave solutions of the Gardner equation in dusty plasmas

In this paper, we mainly study the Gardner equation that models the propagation of dust ion acoustic waves. By using the Exp-function method, abundant traveling wave solutions like bright solitary, bright-dark solitary, dark solitary (type-1, type-2, type-3, type-4) and periodic wave solutions or compact-like solutions (type-1, type-2, type-3, type-4) are constructed. The behaviors of the solutions are illustrated through the 3-D contours and 2D curves. The obtained results show that the proposed method is straightforward, powerful and can provide more forms of the traveling wave solutions, which are expected to be helpful for the study of the traveling wave theory in dusty plasmas.

Automated summary

In this paper, the Gardner equation, which models the propagation of dust ion acoustic waves, is studied. Various traveling wave solutions are constructed using the Exp-function method and their behaviors are illustrated through 3-D contours and 2D curves. The results show that the proposed method is straightforward, powerful, and provides more forms of traveling wave solutions, which are expected to be helpful for the study of traveling wave theory in dusty plasmas.