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We study a general class of spinning pulsating strings in $(AdS_5 \timesS^5)_{\varkappa}$ background. For these family of solitons, we examine thescaling relation between the energy, spin or angular momentum. We verify thatin $\varkappa \rightarrow 0 $ limit these relations reduce to the undeformed$AdS_5 \times S^5$ case. We further study an example of a string which isspinning in the $\varkappa$-deformed AdS$_5$ and S$^5$ simultaneously and findout the scaling relation among various conserved charges.

Spinning pulsating strings in $(AdS_5 \times S^5)_{\varkappa}$