  We study traveling wave solutions of an equation for surface waves of
moderate amplitude arising as a shallow water approximation of the Euler
equations for inviscid, incompressible and homogenous fluids. We obtain
solitary waves of elevation and depression, including a family of solitary
waves with compact support, where the amplitude may increase or decrease with
respect to the wave speed. Our approach is based on techniques from dynamical
systems and relies on a reformulation of the evolution equation as an
autonomous Hamiltonian system which facilitates an explicit expression for
bounded orbits in the phase plane to establish existence of the corresponding
periodic and solitary traveling wave solutions.
