Formation and dynamics of electrostatic solitary waves associated with relativistic electron beam

Properties of nonlinear electrostatic solitary waves in a plasma are analyzed by using the hydrodynamic model for electrons, positrons, and relativistic electron beam. For this purpose, the Kadomtsev-Petviashvili (KP) equation has been derived and its analytical solution is presented. It is found that the nonlinear solitary structures can propagate as slow and fast modes. The dependence of these modes on the plasma parameters is defined numerically. Furthermore, positive and negative electrostatic solitary structures can exist. In order to show that the characteristics of the solitary wave profile are influenced by the plasma parameters, the relevant numerical analysis of the KP equation is obtained. The electrostatic solitary waves, as predicted here, may be associated with the nonlinear structures caused by the interaction of relativistic jets with plasma medium, such as in the active galactic nuclei and in the magnetosphere of collapsing stars.