Figure 1
From: Nonlinear dispersion relation in integrable turbulence
Numerical simulations of the 1-D NLS equation. Three columns correspond to three different values of \(\Gamma\) 0.12, 0.33, and 0.65, respectively. The central frequency of the carrier wave and the initial width of the wave spectrum are set to \(f_0=1.15\) Hz and \(\Delta f = 0.2\) Hz. (a) Spatiotemporal diagram for the complex envelope amplitude \(|\psi (t,z)|\). (b) Corresponding nonlinear dispersion relation \(|{\widetilde{\psi }}(\omega ,k)|^2\) normalized to the maximum. (c) Nonlinear dispersion relation averaged over 1000 realizations and normalized to the maximum. Propagation distance is 500 m. (d) Cross-section of the averaged nonlinear dispersion relation at \(\omega =0\) (along the blue line in c). Dashed purple line shows a Lorentzian fit. In (b–d), vertical black and red dashed lines represent the linear dispersion \(k(\omega )\) and its nonlinear correction of Eq. (5) respectively.
