Solitary waves for the generalized nonlinear wave equation in (3+1) dimensions with gas bubbles using the Nnucci’s reduction, enhanced and modified Kudryashov algorithms

Abstract

In this study, we handled the solitary waves of the generalized nonlinear wave equation in (3+1) dimensions with gas bubbles because liquids with gas bubbles are widespread in engineering, science, life, nature, and physics. The considered model is solved by the enhanced and modified Kudryashov’s methods for obtaining the solitary waves. Nucci’s direct reduction is utilized to extract the first integral and exact solutions of the considered model. Solitary wave solutions and singular soliton solutions were discovered when we employed the enhanced Kudryashov’s method. 3D, contour, and 2D plots are given for some obtained solutions. Based on our work, we can say that the methods discussed are powerful and effective for finding solitary wave solutions to partial differential equations. The resulting exact solutions can be helpful to theoretical investigations of the system under consideration, as they can explain various new wave properties. Our results in this work are essential to describe many oceanographic and physical implementations, including ocean gravity waves and many other related areas.