Solitons in some geometrical field theories

A geometrical approach is developed to two-dimensional field theories, in the framework of which a number of nonlinear models – the theory of gravitation with constant scalar curvature, the massless scalar Born–Infeld field, and also a relativistic string – an be described by a single nonlinear Liouville equation. The soliton solutions of this equation and their stability are investigated. It is shown that such solutions can be interpreted as particles with nonzero rest mass, and this interpretation is valid at both the classical and the quantum level.