Figure 3

Experimental reconstruction of the nonlinear dispersion relation. Four columns correspond to four different values of \(\Gamma\) 0.12, 0.33, 0.65, and 6.18, respectively. (a) Spatiotemporal diagram of the wave envelope amplitude \(|\Psi (t,z)|\). Data received from 20 probes have been post-processed and arranged in 20 vertical rows subtracting waves’ group velocity (\(t=\tau -z/c_g\)). (b) Nonlinear dispersion relation reconstructed from the evolution of the complex wave envelope. \(\Gamma =\) 0.12, 0.33, 0.65 correspond to an initial spectral width \(\Delta f=0.2\) Hz and \(\langle |{\widetilde{\psi }}(\omega ,k)|^2\rangle\) is averaged over several realizations (see “Methods”). In order to observe the signature of a single soliton, the NDR is not averaged for \(\Gamma =6.18\) (corresponding to \(\Delta f=0.037\) Hz). (c) Cross-section of the nonlinear dispersion relation at \(\omega =0\). Dashed purple line shows a Lorentzian fit, blue line shows corresponding results of NLS simulation.