Analytical study of solitons for the variant Boussinesq equations

In this paper, two useful methods that are traveling wave hypothesis and auxiliary function method are constructed new periodic solution, kink soliton solution and bell-shaped solitary wave solution of the variant Boussinesq equations. The existence conditions are given. A pair of solitary wave solutions via the traveling wave hypothesis is mainly studied: the waveform change and the nature of the analysis depending on the choice of solitonic parameters. A new physical phenomenon occurring in this system is the waveform of each soliton gets change or recovery under different parameters, which might provide us with a different approach of load information transfer.