Exact Solitary Wave Solutions of the Generalized Strain Wave Equation in Microstructured Solids and their Impacts on Waveguide Properties via the iB-Function Method

In this work, we employ the implicit Bogning (iB) function method to obtain exact solitary wave solutions in various forms of the generalized strain wave equation in microstructured solids. We investigate the impact of these microstructures on the obtained solutions and introduce new varieties of waveguides via the reduced partial differential equations governing wave propagation. The microstructures are considered solely from a waveguide perspective. To carry out the study, we constructed the wave solutions of nonlinear partial differential equation governing the dynamics in solid microstructures. The control microstructured solids are assumed to be immersed in a medium with variable coefficients. Using the characteristic indices of the iB functions, we determine the forms of the solutions and evaluate the influence of each coefficients. Some solutions dynamics are illustrated graphically through three-dimensional profiles. Our results differ significantly from earlier findings and have not been published elsewhere. They demonstrate that the iB function method is an effective and straightforward mathematical tool for obtaining exact solitary solutions to nonlinear partial differential equations arising in the mathematical physics, materials physics, fiber optics, engineering, and other natural sciences.