Solitons in AdS

The work examines soliton solutions in nonlinear scalar field theories in spaces of constant curvature — anti-de Sitter (AdS), de Sitter (dS), and Lobachevsky (H). It is shown that in AdS_{d+1} space of dimension d ≥ 2, there exist infinite families of soliton configurations for two types of models: deformations of the sine-Gordon theory and deformations of the Mexican hat model. A key role in constructing such solutions is played by the existence of a two-dimensional space of null orthogonal vectors, which allows the construction of solutions with arbitrary functions of ratios of the so-called plane waves (analogous to exponentials in flat space). In dS and H spaces, only single-soliton solutions have so far been constructed.