  We develop an approach for solving the string equations of motion and
Virasoro constraints in any background which has some (unfixed) number of
commuting Killing vector fields. It is based on a specific ansatz for the
string embedding. We apply the above mentioned approach for strings moving
inAdS_3 x S^3 x T^4 with 2-form NS-NS B-field. We succeeded to find solutions
for a large class of string configurations on this background. In particular,
we derive dyonic giant magnon solutions in the R_t x S^3 subspace, and obtain
the leading finite-size correction to the dispersion relation.
