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

Abstract

In this Brief Communication, we present an exact analytic nonlinear dispersion relation (NLDR) for the dust acoustic waves using the Korteweg–de Vries model. The NLDR agrees with the spectrum of spatiotemporal evolution obtained from an exact solution as in Mir et al. [Phys. Plasmas 27, 113701 (2020)]. The NLDR also shows a reasonable match with the experimental data of Thompson et al. [Phys. Plasmas 4, 2331 (1997)] in the long-wavelength limit (kλD≪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.