Pulsating strings in I-brane background

We study pulsating strings both on a single stack of NS5-branes and two orthogonal stacks of NS5-branes (the so called I-brane) by using the Polyakov form of the fundamental string action. For the I-brane background, by using a symmetry that decouples the two spheres from the flat geometry, we study pulsating solutions of the string when it pulsates on both the spheres independently and simultaneously. We finally derive the energy of pulsating strings as a function of adiabatic invariant oscillation number in these cases and studied some limiting cases in detail.