ABSTRACT
This chapter deals with plane one-dimensional relativistic electron oscillations described by the P1RE system of equations. It explains the background of breaking: the shift of the fundamental oscillation frequency and the violation of the property of invariance. The chapter is devoted to the numerical integration of equations with the initial conditions. It presents the calculation formulas of the method, the main purpose of which is to simulate the process of breaking of oscillations. The chapter discusses the relativistic breaking of the electronic oscillations. It describes the use of both asymptotic and numerical methods for simulating the effect of the breaking of electron oscillations in a plasma. The chapter looks at the background of breaking: the shift of the fundamental oscillation frequency and the violation of the property of invariance. In the weakly non-linear approximation using the Lagrangian variables, it is established that the shift of the oscillation frequency quadratically depends on the initial amplitude.
