Subharmonic bifurcations of localized solutions of a discrete NLS equation

Pages: 756 - 767, Issue Special, August 2005

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Vassilis Rothos - School of Mathematical Sciences, Queen Mary College, Mile End, E1 4NS London, United Kingdom (email)

Abstract: Using an analytical approach, we derive an explicit formula for the subharmonic Mel'nikov potential ${\rm L}^{^{{\p}/{\q}}}$ for perturbations of twist maps. Our method based on the integrability of map and the variational approach of twist map. If ${\rm L}^{^{{\p}/{\q}}}$ is non--constant the perturbed twist map is non--integrable and all the resonant curves are destroyed for $\abs{\varepsilon}\ll 1$. We also apply our result to show the existence of such subharmonic bifurcations for a mapping representing localized oscillatory solutions of a discrete NLS equation with conservative and dissipative perturbations.

Keywords:  Twist Maps, Subharmonic Melnikov potential, Discrete NLS.
Mathematics Subject Classification:  Primary: 34C37; Secondary: 34C11, 34C20.

Received: September 2004;      Revised: May 2005;      Published: September 2005.