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We study rigidly rotating and pulsating (m, n) strings in \(AdS_3 \times S^3\) with mixed three form flux. The \(AdS_3 \times S^3\) background with mixed three form flux is obtained in the near horizon limit of SL(2, Z)-transformed solution, corresponding to the bound state of NS5-branes and fundamental strings. We study the probe (m, n)-string in this background by solving the manifest SL(2, Z)-covariant form of the action. We find the dyonic giant magnon and single spike solutions corresponding to the equations of motion of a probe string in this background and find various relationships among the conserved charges. We further study a class of pulsating (m, n) string in \(AdS_3\) with mixed three form flux.

SL(2, Z) invariant rotating (m, n) strings in $$AdS_3\times S^3$$ A d S 3 × S 3 with mixed flux