On the Rotating and Oscillating strings in $(AdS_3\times S^3)_{\varkappa}$

Understand

We study rigidly rotating strings in the $\varkappa$-deformed $AdS_3 \times S^3$ background.

• We find out two classes of solutions corresponding to the giant magnon and single spike solutions of the string rotating in two $S^2_{\varkappa}$ subspace of rotations reduced along two different isometries.
• We verify that the dispersion relations reduce to the well known relation in the $\varkappa\rightarrow 0$ limit.
• We further study some oscillating string solutions in the $S^3_{\varkappa}$ subspace.