Exploration of the soliton solutions of the (n+1) dimensional generalized Kadomstev Petviashvili equation using an innovative approach

In this paper, we deal with the (n+1)-dimensional generalized Kadomtsev-Petviashvili equation (dgKPE). This is an important model in nonlinear science, with applications in various fields. Its integrability and rich soliton dynamics continue to attract researchers interested in the field of nonlinear partial differential equations (NLPDEs). We are interested in the new auxiliary equation method (NAEM). We reduce the equation to an ordinary differential equation (ODE) with the help of an appropriate wave transformation and search for different types of soliton solutions. Additionally, we demonstrated the efficacy of the NAEM as a straightforward yet powerful mathematical instrument for handling challenging issues, highlighting its potential to resolve the challenging problems related to the study of nonlinear equations. This technique yields several types of solutions for (n+1)-dgKPE, including trigonometric, hyperbolic, shock wave, singular soliton, exponential, and rational functions. A range of graphs showcasing the results are reviewed, as well as the wave behavior for the solutions in different circumstances. The obtained data provide important information for studying hydrodynamic waves, plasma fluctuations, and optical solitons. They also aid in understanding the behavior of the KPE in different physical situations. We clarify in this article how the (n+1)-dgKPE, when combined with NAEM, can result in better data transmission rates, optimized optical systems, and the advancement of nonlinear optics toward more dependable and efficient communication technologies. The obtained information clarifies the equation and opens up new avenues for investigation. To our knowledge, for this equation, these methods of investigation have not been utilized before. The accuracy of each solution has been verified using the Maple software program.