Two new types of nonlocal Boussinesq equations in water waves: Bright and dark soliton solutions

In this work, we develop two new types of (1+1)-dimensional nonlocal Boussinesq equations to represent more situations in complex water waves. By applying ansatz method, we construct the explicit soliton solutions for the equations. We give the parameter constraints of the existence of soliton solutions, trivial solutions and complex singular solutions. Moreover, we also investigate the impacts of the system parameter alpha on the solitons.

Automated summary

This work introduces two new types of (1+1)-dimensional nonlocal Boussinesq equations and investigates the parameter constraints and impacts of system parameter α on solitons, offering insights into complex water waves.