New dynamical analysis of the exact traveling wave solutions to a (3+1)-dimensional Gardner-KP equation by three efficient architecture

Abstract

In this research article, the (3 + 1) dimensional nonlinear Gardner- Kadomtsov-Petviashvili (Gardner-KP) equation, demonstrating the nonlinear modulation of periodic waves, has been analyzed using (G'/ G) (G/G(2) )generalized improved (G'/ G) method ) methods and a large number of traveling wave solutions have been generated. These G solutions exhibit structures with physical properties of hyperbolic, trigonometric, and rational solution types. Numerical simulations were performed for the obtained solutions at different values of the parameters. The stability property of the obtained solutions was tested to demonstrate their reliability. Our novelty in this study lies in obtaining distinct and enriched solutions compared to existing literature, conducting a comparative analysis of three methods, and investigating the stability property of solutions for the Gardner-KP equation, which has not been explored in the existing literature.