Abundant analytical optical soliton solutions to the integrable (3+1)-Boussinesq equations

Abstract

In our current work, we will extract abundant analytical optical soliton solutions to the (3+1)-Boussinesq equation ((3+1)-BE) by using three different techniques that are implemented for the first time to this model. The suggested model is the developed one that governs the coastal and ocean engineering waves that involve the nonlinearities and the dispersion terms as the tsunami waves and other versions of solid mechanics waves. The three suggested techniques that will be choosed to extract these unexpected abundant analytical optical soliton solutions to the (3+1)-Boussinesq equation are the extended direct algebraic method (EDAM), the (G′G) -expansion method and the extended simple equation method (ESEM) which are implemented in arranged sequence and with the same vein. Moreover, the novelty of our obtained solutions clear when the comparison is implemented not only between our new extracted abundant analytical optical soliton solutions that are demonstrated by these three methods but also with that established previously by other authors who used other various methods.