Investigations of soliton structures and dynamical behaviors of the Westervelt equation with two analytical techniques

The study of nonlinear partial differential equations is a crucial area of scientific research to understand fundamental properties and common characteristics of nonlinear phenomena. This research focuses on the Westervelt equation and various new soliton structures, which are systematically derived using improved F-expansion and unified approaches. To verify the physical relevance of the results, three-dimensional (3D) and two-dimensional (2D) combined plots are generated by selecting appropriate parameter values, offering more profound insights into the obtained wave solutions. By changing the values of the parameters, we get different types of 3D wave profiles. In addition, the influence of sound diffusivity on the Westervelt equation is examined using 2D-combined plots. We also compare the solutions obtained for our schemes and our solutions with those in the previous literature. Furthermore, the methods employed are efficient and reliable for constructing novel soliton wave solutions in nonlinear physical systems. The findings of this research are expected to have significant applications in medical science, including transducers, contrast agents, pulse compression, beam shaping, tissue harmonic imaging, blood flow and tissue motion measurement techniques, three-dimensional imaging, and several other fields.