ABSTRACT
This chapter deals with plane one-dimensional non-relativistic electron oscillations described by the P1NE system of equations. The main goal is to clarify the conditions under which such oscillations can exist indefinitely. Of particular interest are the ‘axial solutions’ of the P1NE system, as well as solutions of a special type built on their basis. The chapter provides one of the simplest formulations of the initial–boundary value problem for the P1NE equations, which describes free plane one-dimensional non-relativistic oscillatory electron motions. It considers oscillations of the plasma stab, since the boundary conditions prevent any perturbations from moving beyond the boundaries of the segment. For the well-known quasilinear system of hyperbolic equations the so-called axial solutions are studied, i.e., solutions of some auxiliary system of ordinary differential equations.
