Dispersive stability of infinite dimensional Hamiltonian systems on lattices
- Mielke, Alexander
- Patz, Carsten
2010 Mathematics Subject Classification
- 37K60 34Dxx 41A60
- Dispersive decay, oscillatory integrals, discrete Klein--Gordon equation, FPU chain
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 4, then small localized initial data decay like 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 $ell^p$ spaces.
- Appl. Anal., 89 (2010) pp. 1493--1512.