  New exact solution class of Born -- Infeld type nonlinear scalar field model
is obtained. The variational principle of this model has a specific form which
is characteristic for extremal four-dimensional hypersurface or hyper-film in
five-dimensional space-time. Obtained solutions are singular solitons
propagating with speed of light and having energy, momentum, and angular
momentum which can be calculated for explicit conditions. Such solitons will be
called the lightlike ones. The soliton singularity has a form of moving
two-dimensional surface or shell. The lightlike soliton can have a set of
tubelike singular shells with the appropriate cavities. A twisted lightlike
soliton is considered. It is notable that its energy is proportional to its
angular momentum in high-frequency approximation. A case with one tubelike
cavity is considered. In this case the soliton shell is diffeomorphic to a
cylindrical surface with threads by multifilar helix. The shell transverse size
of the appropriate finite energy soliton can be converging to zero at infinity.
The ideal gas of such lightlike solitons with minimal twist parameter is
considered in a finite volume. Explicit conditions provide that the angular
momentum of each soliton in the volume equals Planck constant. The equilibrium
energy spectral density for the solitons is obtained. It has the form of Planck
distribution in some approximation. A beam of the twisted lightlike solitons is
considered. The representation of arbitrary polarization for the beam with the
twisted lightlike solitons is discussed. It is shown that the effect of
mechanical angular momentum transfer to absorbent by the circularly polarized
beam can be provided. This effect is well known for photon beam. Thus the
soliton solution which have determinate likeness with photon is obtained in
particular.
