Symmetry analysis for the (3+1)-dimensional generalized nonlinear evolution equation arising in the shallow water waves

This article delves into the wave dynamics of the (3+1)-dimensional nonlinear model, which serves as a representation of shallow water waves. This model finds relevance in addressing various natural phenomena such as tides, storms, atmospheric flows, and tsunamis, all linked to shallow water waves. These waves, often called long water waves, exhibit a considerable wavelength relative to their depth. The Lie group method ensures a wide range of wave structures. This method is a recognized and dependable mathematical technique for obtaining precise solutions to nonlinear partial differential equations across various domains. Its applications span fields such as mathematical physics, nonlinear dynamics, oceanography, engineering sciences, and numerous other disciplines. Furthermore, we elucidate the physical implications of certain solutions by generating 2D and 3D graphs using the corresponding parameter values.

Automated summary

This article explores the wave dynamics of a (3+1)-dimensional nonlinear model, which represents shallow water waves. This model is relevant for understanding phenomena such as tides, storms, atmospheric flows, and tsunamis. The Lie group method is used to obtain precise solutions to nonlinear partial differential equations in various domains. Its applications span across mathematical physics, nonlinear dynamics, oceanography, and engineering sciences. 2D and 3D graphs are generated to illustrate the physical implications of specific solutions.