Figure 2
The renormalized vibrations in FPU-β-like DNLS model with size N = 32. The blue solid curve is the dispersion relation \({\omega }_{k}=4\,{\sin }^{2}(k\mathrm{/2})\) of Eq. (2) for linear system. The empty and filled circles are the numerical data of renormalized vibrations in (e, s) parameter spaces with (0.422, 0.5) and (1.238, 0.5). The dotted and dash-dotted curves are the renormalized dispersion relations \({\omega }_{k}^{R}=\alpha {\omega }_{k}\) from renormalization theory, where the renormalization coefficients α’s are calculated from Eq. (5) as α = 1.966 and α = 3.066, respectively. Perfect agreements between numerical simulations and renormalization theory are obtained.
