In this paper, the theoretical model of weak decaying collective excitations characteristic of many-particle systems with long-range interaction potentials is developed using the example of one-component strongly coupled Yukawa plasmas. The proposed model is based on the self-consistent relaxation theory of collective dynamics and covers spatial scales from extended hydrodynamics to scales related to the mean interparticle distance. The theoretical model reproduces the dynamic structure factor spectra and the corresponding dispersion characteristics in agreement with molecular dynamics simulation data without using any fitting parameters. In the limit of small wave numbers, the correspondence of the proposed theoretical model with the damped harmonic oscillator model is established. The simple analytical expression for the sound attenuation coefficient of strongly coupled Yukawa plasmas is obtained.

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• Collective behavior
• Long-range interactions
• Plasma oscillations
• Sound waves
• Collective dynamics
• Disordered systems
• Molecular dynamics