Periodic soliton solutions of the nonlinear Schrödinger equation with variable nonlinearity and external parabolic potential

We derive novel analytical solutions that describe periodic solitons in one-dimensional nonlinear Schrödinger equation with a variable nonlinearity coefficient and an external parabolic potential coefficient. We establish an integrability condition that connects these coefficients. We discuss the propagation properties of these periodic solitons under nonlinearity management. Our results demonstrate that the periodic solitons can be controlled by selecting appropriately the nonlinearity coefficient.