  An exact analytical model of the process of collision and nonlinear
interaction of gravitational and/or electromagnetic soliton wave and strong
non-soliton electromagnetic traveling wave of arbitrary profile propagating in
the expanding universe (the symmetric Kasner spacetime) is presented. In
contrast to intuitive expectations that rather strong traveling waves can
destroy the soliton, it occurs that the soliton survives during its interaction
with electromagnetic wave of arbitrary amplitude and profile, but its
parameters begin to evolve under the influence of this interaction. If a
traveling electromagnetic wave possesses a finite duration, the soliton
parameters after interaction take constant values again, but these values in
general are different from those before the interaction. Based on exact
solutions of Einstein - Maxwell equations, our model demonstrates a series of
nonlinear phenomena, such as (a) creation of gravitational waves in the
collision of two electromagnetic waves, (b) creation of electromagnetic soliton
wave in the collision of gravitational soliton with traveling electromagnetic
wave, (c) scattering of a part of soliton wave in the direction of propagation
of traveling electromagnetic wave, (d) quasiperiodic oscillating character of
fields in the wave interaction region and multiple mutual transformations of
gravitational and electromagnetic waves in this region. The figures illustrate
these features of nonlinear wave interactions in General Relativity.
