Building novel solitary wave solutions for the generalized non-linear (3+1)-dimensional wave equation with gas bubbles in fluids using an analytic method

This article investigates the generalized nonlinear (3+1)-dimensional wave equation using an analytical technique — the Extended F-expansion method — to derive a variety of exact wave solutions and analyze the dynamic behavior of distinct wave profiles. The study presents several types of soliton solutions, including dark, bright, singular, periodic, and singular periodic forms. To the best of our knowledge, these specific solutions have not been previously reported in the literature. By assigning appropriate values to the free parameters, the behavior of the obtained solutions is illustrated through two- and three-dimensional plots, as well as corresponding contour diagrams. The proposed analytical method not only contributes to the theoretical understanding of nonlinear wave phenomena but also demonstrates practical relevance in applied sciences, particularly in fluid mechanics and engineering contexts involving gas-liquid interactions.