Novel wave behaviors of the generalized Kadomtsev–Petviashvili modified equal width-burgers equation via modified mathematical methods

In this paper, we have employed two different forms of mathematical methods, namely the extended simple equation method, and modified [Formula: see text]-expansion method to establish several types of solutions of the generalized Kadomtsev–Petviashvili modified equal width-Burgers (G-KP-MEW-B) equation that is used to designate the propagation of long-wave with dissipation and dispersion in nonlinear media. A suitable transform is applied to convert into an ordinary differential equation. As a result, after implementation of the proposed schemes, distinct types of solutions are obtained in the form of exponential hyperbolic, trigonometric and rational functions. To analyze the physical phenomena of the model, some constructed solutions are plotted in 2-dimensional and 3-dimensional by inserting the specific values to attached parameters. Hence, the recommended schemes are highly admirably mathematical tools to evaluate the wave solutions of various models in nonlinear science.