Authors: Hafiz Muhammad Ameer and Muhammad Iqbal

JSA-Vol. 3 (2024),

Abstract: The main focus of this article is to develop new wave structures for non-linear evolution equations. These equations are becoming increasingly common in several kinds of domains, such as fluid dynamics, wave theory, quantum mechanics, non-linear optics, and mathematical biological models. To solve the Davey Stewartson Kadomtsev Petviashvili equation, we have employed a modified Khater method to generate a number of different forms of soliton wave structures. It is important to obtain precise solutions to this equation in order to completely understand the dynamics of waves in a physical model. The obtained results shed light on the dynamic behavior of wave structures, which includes the solutions for brilliant, single, dark, and periodic singular solitons. We plot some of the chosen solutions in both two and three-dimensional graphs to illustrate their behavior. These innovative concepts utilize symbolic computations to offer comprehensive and powerful mathematical tools for addressing various benign nonlinear problems.