Nonlinear dispersion relation of dust acoustic waves using the Korteweg-de Vries model

In this brief communication, we present an exact analytic nonlinear dispersion relation (NLDR) for the dust acoustic waves using the Korteweg-de Vries (KdV) model. The NLDR agrees with the spectrum of spatio-temporal evolution obtained from an exact solution as in Mir~\textit{et al.}~[Phys. Plasmas \textbf{27}, 113701 (2020)]. The NLDR also shows a reasonable match with the experimental data of Thompson~\textit{et al.}~[Phys. Plasmas \textbf{4}, 2331 (1997)] in the long wavelength limit ($k \lambda_D \ll 1$). We suggest that such nonlinear corrections should be incorporated in the dispersion relation along with damping, streaming, and correlation effects in order to provide a more realistic interpretation of experimental data.