Melnikov Analysis for Singularly Perturbed DSII Equation

Details Melnikov Analysis for Singularly Perturbed DSII Equation Melnikov Analysis for Singularly Perturbed DSII Equation

2002-06-25

arxiv.org/abs/math/0206272v1

Mathematics

Analysis of PDEs

Scientific paper

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 a Melnikov measurement.

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