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.
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Mielke et al. (2010) studied this question.
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