2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/64397Rigorous Melnikov analysis is accomplished for Davey-Stewartson II equation under singular perturbation. Unstable fiber theorem and center-stable manifold theorem are established. The fact that the unperturbed homoclinic orbit, obtained via a Darboux transformation, is a classical solution, leads to the conclusion that only local well-posedness is necessary for a Melnikov measurement.Analysis of PDEsMathematical PhysicsDynamical Systems35Q55, 35Q30text