On particle type string solutions in AdS₃ x S³

The AdS_3 x S^3 string dynamics is described in a conformal gauge using the SL(2,R) and SU(2) group variables as the target space coordinates. A subclass of string surfaces with constant induced metric tensor on both AdS_3 and S^3 projections is considered. The general solution of string equations on this subclass is presented and the corresponding conserved charges related to the isometry transformations are calculated. The subclass of solutions is characterized by a finite number of parameters. The Poisson bracket structure on the space of parameters is calculated, its connection to the particle dynamics in SL(2,R) x SU(2) is analyzed and a possible way of quantization is discussed.