The nonlinear Schrodinger equation is solved on an infinitesimal thin
ring or circle. We obtained the exact real wave functions with their c
orresponding energies for the ground state and the excited states. Cri
tical values of the circle perimeter are found at which the ground sta
te changes its structure and additional higher excited states appear.
Also, the complex wave functions that correspond to energy levels with
finite angular momentum are studied.