New symmetric bidirectional progressive surface-wave solutions to a generalized fourth-order nonlinear partial differential equation involving second-order time-derivative
Marwan Alquran
Abstract
New nonlinear fourth-order integrable equation of second-order in time has been established by Wazwaz via collaborating some recursion operators and the sense of Boussinesq equation. The proposed new equation has several real-life applications in the field of water-waves, such as gravity-capillary waves, waves in shallow water, and ocean engineering. The aim of the current study is threefold. First, we show that the propagation of Wazwaz equation is simultaneously moving symmetric bidirectional waves. Second, we extract new novel solutions such as bidirectional lumps and bidirectional kinks, singular-kinks, and periodic-kinks. Finally, by using graphical analysis, we show the physical structures of the recovery solutions and study the significance of the model’s parameters.