Optical soliton solutions of nonlinear differential Boussinesq water wave equation via two analytical techniques

In this article, we examine the optical soliton solutions of the 4th-order nonlinear Boussinesq water wave equation using the modified (G′/G2)− expansion and F-expansion methods. We utilize the similarity transformation to transform the partial differential form of the equation into an ordinary differential form. These techniques present a variety of solutions, including bright, dark, singular, dark-periodic, and singular-periodic soliton solutions. We plot the derived solutions in several profiles, such as 2D, 3D, and contour, to illustrate their physical appearance. The determined findings might be useful and have an enormous effect on the research of nonlinear phenomena in a variety of physical areas of science, like shallow water waves, acoustics, fluid dynamics, laser optics, communication systems, and heat transfer. The achieved results demonstrate the validity, applicability, and effectiveness of the presented method. We plot and validate the found solutions using the computational program MATHEMATICA. •We exploring new solution of Boussinesq water wave equation like analytical wave solitons, bright, dark, singular, dark-periodic and singular-periodic optical solitons.•Analytical techniques like modified (G′/G2)− expansion and F-expansion technique.•Partial differential equations have been considered because of their important applications in nonlinear science and engineering.•It has great importance to seek the wave phenomena that they describe in shallow water.•In this paper, we also present the propagation of waves in 2D, 3D and contour graphs.•We hope that our results are going to be useful for applied sciences in forward studies.