Pulsating string solution and stability in two parameter χ-deformed background

A bstract In this paper, we investigate pulsating string solutions within the context of two parameter χ -deformed R R × S 2 background. We derive the energy and oscillation number relation for the deformed R R × S 2 in short string limit. Additionally, we derive the first order perturbation equation for pulsating string in this specific background. As a special case of the two parameter deformed background, we examine the stability of the pulsating string solution in one parameter deformed R R × S 2 and AdS 3 background by setting one of the deformation parameters to zero.