Abstract
Rigorous 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 such a Melnikov analysis. The main open issue regarding a proof of the existence of a homoclinic orbit to the perturbed Davey–Stewartson II equation is discussed in the Appendix.
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