Abstract
The formation of nonlinear, nonstationary structures in weakly collisional media with collective interactions are investigated analytically within the framework of the kinetic description. This issue is considered in one-dimensional geometry using collision integral in the Bhatnagar-Gross-Krook form and some model forms of the interparticle interaction potentials that ensure the finiteness of the energy and momentum of the systems under consideration. As such potentials, we select the Yukawa potential, the δ-potential, which describes coherent structures in a plasma. For such potentials we obtained a dispersion relation which makes it possible to estimate the size and type of the forming structures.
Highlights
We examined the formation of coherent structures in the environment, consisting of a Maxwellian ensemble of particles
In our model of collisional medium we have used some physically admissible forms of the interparticle interaction potentials providing the finiteness of the energy and momentum of the systems under consideration
We applied the method of constructing time-dependent solutions of the kinetics equations based on the expansion of the distribution function as a series in positive powers of the interparticle interaction potentials [8]
Summary
There are a lot of natural systems which are capable of exchanging energy and negentropy with the immediate environment [1,2]. A well-known example of dissipative processes is the BeloysovGhabotinskyl reaction [2,3], whereas the formation of nonlinear wave-like vortex-like structures in the collisionless Coulomb plasmas [4,5] is the most vivid and vital sample of the system with the purely potential interaction between particles, which have been described by soliton-like distributions. In this case, one should keep in mind that such wave-like solutions possess some properties of particles [6,7]. Various potentials of interaction between particles are considered
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