An innovative approach for developing the precise traveling wave solutions to a family of 3D fractional WBBM equations

Abstract

The Wazwaz–Benjamin–Bona–Mahony (WBBM) equations are solved in this paper using an explicit and precise soliton method. In water wave mechanics, fluid dynamics, ocean engineering, and science, the wave phenomena of the resulting solutions are used. The WBBM model did not employ the new auxiliary equation (NAE) technique. We used this approach to generate a large number of analytical solutions to define explicit functions with free parameters that were hyperbolic, trigonometric, and trigonometric in nature. This study also addresses the impact of the wave phenomenon in two-dimensional (2D) diagrams. It includes several plots in three-dimensional (3D) surface plots and contour plot graphs illustrating the acquired answers. In contrast, we have contrasted our response with those found in earlier works of literature. Therefore, it is clear that the technique mentioned above may be a possible tool for developing novel, accurate solutions for various NLEEs, which are crucial in applied research and engineering. The findings were gathered to assess the capability of the finished method to compute the precise solutions of the WBBM equations that can be used to implement the nonlinear water model in the ocean and coastal engineering. By substituting their respective equations with the computational program Mathematica, all of the solutions provided have been verified.

Keywords

• The new auxiliary equation method
• Wazwaz–Benjamin–Bona–Mahony​ equation
• Solitary wave
• Exact solution
• Soliton shape