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The Hamiltonian approach to cosmological perturbations in general relativity in finite space-time is developed, where a cosmological scale factor is identified with spatial averaging the metric determinant logarithm. This identification preserves the number of variables and leads to a cosmological perturbation theory with the scalar potential perturbations in contrast to the kinetic perturbations in the Lifshitz version which are responsible for the "primordial power spectrum" of CMB in the inflationary model. The Hamiltonian approach enables to explain this "spectrum" in terms of scale-invariant variables and to consider other topical problem of modern cosmology in the context of quantum cosmological creation of both universes and particles from the stable Bogoliubov vacuum.

The relativistic string model is investigated in a space-time of a constant curvature (de Sitter universe). The fundamental differential quadratic forms of the world surface of the string are considered as the dynamical variables. The coefficients of these forms obey two nonlinear equations 9,ιι~9,22 = e φ cosθ + Ke~φ, Θ tll -θ ί22 = e φ smθ.

The problem of scattering of two plane waves is exactly solved in the Born-Infeld electrodynamics. The shape and the direction of the plane waves after scattering turn out to be unchanged. There is only a change in the wave phase by the value which is the product of its frequency and the momentum of the incident wave. It is shown that in the interaction region the solution becomes a multiplevalued function of x, t when the electromagnetic field exceeds a certain value which plays the role of an absolute field scale.