Boussinesq-Like Equations: A Class of Soliton Solutions Occurs in Coastal and Ocean Engineering

The Boussinesq equation describes water with small amplitudes and long waves, which is one of the most famous nonlinear evolution equations. Boussinesq-type equations have become crucial for predicting wave transformations in coastal areas since dispersion, time dependence, and weak nonlinearity terms are included in the equation. Here, the Boussinesq-like equations by using the m+1/G′-expansion approach are investigated. In this work, we try to offer complexiton solutions to the studied types of Boussinesq equations and reveal the efficiency of this method to construct soliton solutions. The exact solutions for the Boussinesq-like equations, including spatiotemporal dispersion, are computed using this method. Complexiton traveling wave solutions in the forms of kink, singular, periodic, and periodic-lump are obtained through calculations. The graphs of these solutions are drawn and analyzed to better understand and analyze these gained solutions. Moreover, the existence of all solutions is verified, and to our knowledge, the solutions are novel.