On the existence and conditional energetic stability of solitary water waves with weak surface tension

Abstract

An existence and stability theory for solitary water waves with weak surface tension has recently been given by Buffoni (2005, 2009) [2,3]. The theory, which is variational in nature, relies upon the assumption that the infimum of the variational functional is strictly subhomogeneous with respect to a small parameter. In this Note we rigorously establish the relevant strict-subhomogeneity property and thus complete Buffoni's theory.