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$SL(2,mathbb{Z})$ invariant action for probe $(m,n)$ string in $AdS_3times S^3times T^4$ with mixed three-form fluxes can be described by an integrable deformation of an one-dimensional Neumann-Rosochatius (NR) system. We present the deformed features of the integrable model and study general class of rotating and pulsating solutions by solving the integrable equations of motion. For the rotating string, the explicit solutions can be expressed in terms of elliptic functions. We make use of the integrals of motion to find out the scaling relation among conserved charges for the particular case of constant radii solutions. Then we study the closed $(m,n)$ string pulsating in $R_ttimes S^3$. We find the string profile and calculate the total energy of such pulsating string in terms of oscillation number $(cal{N})$ and angular momentum $(cal{J})$.
Sigma model in $AdS_3times S^3$ background supported by both NS-NS and R-R fluxes is one of the most distinguished integrable models. We study a class of classical string solutions for $N$-spike strings moving in $AdS_3 times S^1$ with angular moment
We address the question about the exact form of the dispersion relation for light-cone string excitations in string theory in AdS3 x S3 x T4 with mixed R-R and NS-NS 3-form fluxes. The analogy with string theory in AdS5 x S5 suggests that in addition
We study the finite size effect of rigidly rotating strings and closed folded strings in $AdS_3times S^3$ geometry with NS-NS B-field. We calculate the classical exponential corrections to the dispersion relation of infinite size giant magnon and sin
Neumann-Rosochatius system is a well known one dimensional integrable system. We study the rotating and pulsating string in $AdS_4 times mathbb{CP}^3$ with a $B_{rm{NS}}$ holonomy turned on over $mathbb{CP}^1 subset mathbb{CP}^3$, or the so called Ah
The type IIB supergravity AdS_3 x S^3 x T^4 background with mixed RR and NSNS 3-form fluxes is a near-horizon limit of a non-threshold bound state of D5-D1 and NS5-NS1 branes. The corresponding superstring world-sheet theory is expected to be integra