Impact of collisions on the dynamics of waves of finite amplitude in a plasma

The problem of determining wave dynamics, considering the evolution of nonlinear waves of finite amplitude in a weakly collisional, Maxwellian plasma, is the focus of this article. Considering this medium with a certain interaction potential associated with a certain limited core of pairwise interaction, the dynamics of the distribution function was studied using the Vlasov equation. Collisions of electrons with neutral particles are described using the collision integral in the Bhatnagar — Gross — Krook form. Having constructed its particular solution and the equilibrium distribution function in the form of a series, an equation was obtained that makes it possible to determine the potential function. Considering the case of a Maxwellian plasma, an integral potential equation was obtained. Based on it, an equation was constructed that determines the perturbation of the potential relative to the spatially homogeneous one. At the same time, this perturbation appears due to the existence of some spatial-temporal stable structure. Based on this, a dispersion relation was obtained, which makes it possible to estimate the spatial scales of the coherent structure.