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mass: Existence and asymptotics
Orbitally but not asymptotically stable ground states for the discrete
We consider examples of discrete nonlinear Schrödinger
equations in $\Z$ admitting ground states which are orbitally but
not asymptotically stable in l $^2(\Z )$. The ground states
contain internal modes which decouple from the continuous modes.
The absence of leaking of energy from discrete to continues modes
leads to an almost conservation and perpetual oscillation of the
discrete modes. This is quite different from what is known for
nonlinear Schrödinger equations in $\R ^d$. To achieve our goal we
prove a Siegel normal form theorem, prove dispersive estimates for
the linearized operators and prove some nonlinear estimates.