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) , 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. © 2013 Elsevier Inc.
Duruk Mutlubaş, N., & Geyer, A. (2013). Orbital stability of solitary waves of moderate amplitude in shallow water. Journal of Differential Equations, 255(2), 254–263. https://doi.org/10.1016/j.jde.2013.04.010