Dispersive stability of infinite-dimensional Hamiltonian systems on lattices

Abstract

We derive dispersive stability results for oscillator chains like the FPU chain or the discrete Klein–Gordon chain. If the nonlinearity is of degree higher than four, then small localized initial data decay exactly as in the linear case. For this, we provide sharp decay estimates for the linearized problem using oscillatory integrals and avoiding the nonoptimal interpolation between different ℓ ^p spaces.

Keywords:

• dispersive decay
• oscillatory integrals
• discrete Klein–Gordon equation
• FPU chain

AMS Subject Classifications::

• 37K60
• 34Dxx
• 41A60

Acknowledgements

The research was partially supported by the Deutsche Forschungsgemeinsschaft under Mie 459/4-3.