Nonrelativistic pulsating strings

We explore nonrelativistic (NR) pulsating string configurations over torsion Newton-Cartan (TNC) geometry having topology R × S² and check the corresponding analytic integrability criteria following Kovacic's algorithm. In the first part we consider pulsating strings propagating over TNC geometry whose world-sheet theory is described by relativistic CFTs. We compute conserved charges associated with the 2D sigma model and show that the classical phase space corresponding to these NR pulsating string configurations is Liouvillian integrable. Finally, we consider nonrelativisitc scaling associated with the world-sheet d.o.f. and show that the corresponding string configuration allows even simpler integrable structure.