Dynamic soliton solutions for the modified complex Korteweg-de Vries system

Abstract

In this study, we studied the (2+1)-dimensional complex modified Korteweg-de Vries (cmKdV) system using the improved Ricatti equation method. cmKdV are nonlinear and coupled partial differential equations that arise in various fields of applied science and engineering, such as ferromagnetic materials and optical fibers. When the method is applied to cmKdV, we successfully derive exact soliton solutions that accurately describe the wave propagation behavior of the system under consideration. The obtained results include trigonometric and hyperbolic function solutions. The results obtained are concise and offer a deeper insight into the dynamics and characteristics of cmKdV. Traveling wave solitons are plotted in 2D and 3D to demonstrate the wave propagation phenomena in the cmKdV model, which are in the form of kink, bright, dark, singular solitons, and periodic solitary wave structures. The method recovers many solutions compared with the existing methods in the literature, indicating that the proposed method is a powerful and valuable approach for achieving analytical solutions to a wide range of nonlinear partial differential equations