On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Abstract In this work, we take into account the (2 + 1)-Davey Stewartson equation (DSE) and (2 + 1)-Complex Coupled Maccari System (CCMS) and their analytical solutions. Besides, we tackle with the role of the problem parameters on the soliton behavior which the investigated DSE produces. Exact traveling wave solutions are highly useful in numerical and analytical theories in such equations. We use an efficient analytical approach to calculate the soliton solutions of these models. We have shown that soliton solutions’ features can represent the spread of propagation on the wave fronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three and two-dimensional arrangements can also be described in graphic representations for their behavior. The results show that the technique is easy applicable, efficient, reliable, robust and categorical when it comes to find exact solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant effects on the behavior of the solitons of the DSE and this examination is studied for the first time in this article.