  A new modified model of nonlinear arcsin-electrodynamics with two parameters
is proposed and analyzed. We obtain the corrections to the Coulomb law. The
effect of vacuum birefringence takes place when the external constant magnetic
field is present. We calculate indices of refraction for two perpendicular
polarizations of electromagnetic waves and estimate bounds on the parameter
$\gamma$ from the BMV and PVLAS experiments. It is shown that the electric
field of a point-like charge is finite at the origin. We calculate the finite
static electric energy of point-like particles and demonstrate that the
electron mass can have the pure electromagnetic nature. The symmetrical
Belinfante energy-momentum tensor and dilatation current are found. We show
that the dilatation symmetry and dual symmetry are broken in the model
suggested. We have investigated the gauge covariant quantization of the
nonlinear electrodynamics fields as well as the gauge fixing approach based on
Dirac's brackets.
