Periodic traveling wave, bright and dark soliton solutions of the (2+1)-dimensional complex modified Korteweg-de Vries system of equations by using three different methods

Abstract

In this paper, the (2+1)-dimensional complex modified Korteweg-de Vries (cmKdV) equations are studied using the sine-cosine method, the tanh-coth method, and the Kudryashov method. As a result, analytical solutions in the form of dark solitons, bright solitons, and periodic wave solutions are obtained. Finally, the dynamic behavior of the solutions is illustrated by choosing the appropriate parameters using 2D and 3D plots. The obtained results show that the proposed methods are straightforward and powerful and can provide more forms of traveling wave solutions, which are expected to be useful for the study of the theory of traveling waves in physics.

Keywords

• periodic traveling wave
• bright soliton
• dark soliton
• sine-cosine method
• tanh-coth method
• kudryashov method