New wave solutions of an integrable dispersive wave equation with a fractional time derivative arising in ocean engineering models - Ali Tozar; Ali Kurt; Orkun Tasbozan (Kuwait Journal of Science)
It is complicated to analyze many events taking place in nature. Idealization which can be defined as neglecting the nonlinear parts of the event can be used to facilitate a deterministic perspective to our understanding of the nature. However, this approximation usually doesn't work when interactions are fully nonlinear. Oceans are the best examples of the systems where interactions are nonlinear. In order to evaluate such systems, unique differential equations are needed. Camassa-Holm equation is one of the most attractive unique differential equation due to its integrability. In this paper, the new wave solutions of  fractional Camassa-Holm equation that generally used as a powerful tool in computer simulation of the water waves in shallow water, coastal and harbor models are obtained by using the new extended direct algebraic method. A completely new thirty-six solutions were obtained and were graphically represented. These solutions can be inspiring for future researchers.