Neumann-Rosochatius system for strings on I-brane

We study rigidly rotating and pulsating strings in the background of a 1+1 dimensional intersection of two orthogonal stacks of fivebranes in type IIB string theory by using the Neumann-Rosochatius (NR) model. Starting with the Polyakov action of the probe fundamental string we show that a generalised ansatz reduce the system into the one dimensional NR model in the presence of flux. The integrable construction of the model is exploited to analyze the rotating and oscillating string solution. We render the large $J$ BMN-type expansion for the energy of rotating string states while the same for the oscillating string has been derived in long string and small angular momenta limit.