American Institute of Mathematical Sciences

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2005, 2005(Special): 756-767. doi: 10.3934/proc.2005.2005.756

Subharmonic bifurcations of localized solutions of a discrete NLS equation

Vassilis Rothos 1,

1. 

School of Mathematical Sciences, Queen Mary College, Mile End, E1 4NS London, United Kingdom

Received  September 2004 Revised  May 2005 Published  September 2005

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: Discrete NLS., Twist Maps, Subharmonic Melnikov potential.
Mathematics Subject Classification: Primary: 34C37; Secondary: 34C11, 34C2.
Citation: Vassilis Rothos. Subharmonic bifurcations of localized solutions of a discrete NLS equation. Conference Publications, 2005, 2005 (Special) : 756-767. doi: 10.3934/proc.2005.2005.756
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