Abstract
The variant Boussinesq and the Lonngren wave equations are underlying to model waves in shallow water, such as beaches, lakes, and rivers, as well as electrical signals in telegraph lines based on tunnel diodes. The aim of this study is to accomplish the closed-form wave solutions by means of the generalized Kudryashov technique to the formerly stated models. The process provides further generic and inclusive wave solutions integrated with physical parameters and for definite values of these constraints reveal distinct special shapes of the waveform, namely kink soliton, bell-shape soliton, singular soliton, anti-bell shape soliton, flat soliton, and other different types of soliton. To estimate the topography of solitons' form, we have outlined 3D and contour plots of some of the defined solutions. It has been demonstrated that the technique used to investigate nonlinear evolution equations (NLEEs) is consistent, compatible, and significant and yield typical and further generic wave solutions. Moreover, the method shows a comprehensive extension of application to function the other types of nonlinear wave phenomena.