Studying the periodic solitary, rational solitary and solitary waves of the nonlinear (2+1)-dimensional Maccari couple model in water wave dynamics

Abstract The analytical and explicit solutions to nonlinear partial differential models are quite an interesting area in nonlinear sciences. The new ansatz transformation on Riccati equation rational expansion method is implemented in this study to ascertain the exact, periodic solitary and solitary wave solutions of the nonlinear (2+1)-dimensional Maccari couple model. By selecting appropriate values for the constant parameters, the dynamic behaviors of some chosen solutions are displayed in terms of 3-D, 2-D, and contour plots. The results indicate that the suggested approach is easy to understand, effective and basic, which is anticipated to provide some fresh ideas for the investigation of traveling wave solutions.