2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/104746We prove short-time existence of smooth solutions for a class of nonlinear, and in general spatially nonlocal, Hamiltonian evolution equations that describe the self-interaction of weakly nonlinear scale-invariant waves. These equations include ones that describe weakly nonlinear hyperbolic surface waves, such as nonlinear Rayleigh wavesAnalysis of PDEsMathematical Physics74J30; 35L60; 74J15text