Wave propagation patterns for the (2+1) dimensional modified complex KDV system via new extended direct algebra method

In this article, we derive various exact solutions and patterns for the complex modified Korteweg–De Vries system of equation (cmKdV) with a generalized innovative extended direct algebra method. The Korteweg-De Vries system exhibits the scientific dynamics of water particles at the surface and beyond the surface level. The system also has applications in ferromagnetic materials, nonlinear optics, and solitons theory. The innovative direct algebra method is applied to obtain dark, multiple, singular, breather and bright wave patterns. This method also provides staggering wave solutions for the complex modified Kortweg-De Vries system in the form of hyperbolic and trigonometric functions. These recovered solutions for the considered model and are more efficient, concise and general than the extant ones. The wave patterns are properly explained with 2-D and 3-D graphs to elucidate wave behaviour for some selected solutions derived for the system. Lastly, the solutions in this work will greatly advance various fields of application of the Kortweg-De Vries equation like optical fibres, ferromagnetic materials, nonlinear optics, signal processing, water waves, plasma physics, soliton theory, string theory and other contemporary sciences.