On solitary-wave solutions of fifth-order KdV type of model equations for water waves

The paper concerns capillary-gravity surface waves propagating on a two-dimensional incompressible and inviscid fluid with or without an obstacle placed at flat horizontal bottom. Formally second-order correct model equations, analogous to the first-order KdV equation, are derived under classical assumptions of long wavelength small amplitude waves. equations fifth-order type where bottom introduces forcing terms in equations. If is zero, equation can possess special Hamiltonian structure after BBM term introduced. existence set stability solitary-wave solutions for KdV-BBM studied. included, only case considered, which forced (also called Kawahara equation) models water when both tension wave speed near their critical values. some large obtained Lyapunov proved. Other studied numerically.