On the Wave Structure Near an Elementary Charge in the Theory of Space-Time Film

Within the framework of the nonlinear field model of the extreme space-time film, its linearization is considered on the background of a spheroidal soliton or spheron, representing an elementary electric charge. The representation of the system of first-order equations for the space-time film in the form of a single equation in hypercomplex form and its linearization on the background of a spheron are obtained. The problem of finding weak wave modes against the background of a spheron is reduced to solving a second-order differential equation. The solution is sought by expanding into an asymptotic series in inverse powers of the radius in a spherical coordinate system. A recurrent formula for the series is obtained. The possibility of the existence of a discrete frequency spectrum of wave modes is shown by means of numerical experiments with partial sums of the series. The possibility of representation of charge elementary particles by soliton solutions containing an elementary charge and wave modes is discussed.