Nonlinear dispersion relation for the finite-amplitude dust acoustic modes is obtained taking into account resonant particle trapping in the wave. The kinetic model predicts a frequency shift scaling $\propto \sqrt{\varphi }$ relative to the linear dispersion relation with $\varphi$ being the wave amplitude of the electrostatic potential. The species contributions to the nonlinear frequency shift have opposite sign: positive for trapped electrons and ions and negative for particles. It is shown that the relative importance of these contributions depends on the electron-to-ion or particle temperature ratio, particle charge, and Havnes parameter. In typical complex plasma experiments, the kinetic frequency shift is dominated by the positive ion contribution. As a result, the nonlinear modification of the dispersion relation affects the wave dispersion properties and may provide the acoustic-like behavior to the wave number domain $k{\lambda }_{Di}\sim 1$.

• Received 20 May 2020
• Accepted 8 July 2020

DOI:https://doi.org/10.1103/PhysRevE.102.023201