Melnikov Analysis for Singularly Perturbed DSII Equation
Analysis of PDEs
2007-05-23 v1 Mathematical Physics
Dynamical Systems
math.MP
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 a Melnikov measurement.
Keywords
Cite
@article{arxiv.math/0206272,
title = {Melnikov Analysis for Singularly Perturbed DSII Equation},
author = {Yanguang Charles Li},
journal= {arXiv preprint arXiv:math/0206272},
year = {2007}
}