Abstract
Since quark-gluon plasma was discovered, it has been called the new state of matter, prompting the beginning of the study of collective effects. Continuing this topic, the oscillation modes of internal waves in a quark-gluon plasma have been investigated. The medium of a quark-gluon plasma is considered an ideal fluid with a small viscosity. The viscosity is taken into account using a dielectric function with a viscosity parameter, which is related to the entropy, and this parameter can be chosen in accordance with different theoretical approaches to describing a quark-gluon plasma. The problem was solved in the long-wavelength limit, but this solution corresponds to the physical case described in the article. This approach reduces the problem to non-linear algebraic equations that were solved using software for numerical calculations. For illustration, the oscillation modes of a viscous quark-gluon plasma are compared with the oscillation modes of a collisional quark-gluon plasma - this will show the effect of the parameter of the dielectric function, which takes into account only viscosity. The solutions are presented in the form of graphs of frequency versus wavenumber, in which you can clearly see the oscillatory waves. Also, these vibrational modes can be used to judge the nature of the waves, and for physical interpretation.