Electron-positron plasma: kinetic symmetries and exact solutions - Taranov, V.B. (Вопросы атомной науки и техники, 2007)
Kinetic model for the high frequency electron-positron plasma waves is considered. Continuous symmetry transformations are found for the model by the indirect method, i.e. from the symmetries of the infinite set of equations for the moments of distribution functions. These symmetries, in combination with discrete ones, determine the form of the possible exact solutions, e.g. traveling waves and self similar local solutions determining the wave structure in the vicinity of its critical points. It is shown that the simplest form of extended symmetry is characteristic for this model. However, the extended symmetry is removed by the indirect moments method, since this symmetry is incompatible with the global conditions of the distribution functions non negativity and the existence of their moments.