Orbital stability of solitary waves of moderate amplitude in shallow water

We study the orbital stability of solitary traveling wave solutions of an equation for surface water waves of moderate amplitude in the shallow water regime. Our approach is based on a method proposed by Grillakis, Shatah and Strauss (1987) [1], and relies on a reformulation of the evolution equation in Hamiltonian form. We deduce stability of solitary waves by proving the convexity of a scalar function, which is based on two nonlinear functionals that are preserved under the flow.