Periodic waves for the cubic-quintic nonlinear Schrodinger equation: Existence and orbital stability

<p style='text-indent:20px;'>In this paper, we prove existence and orbital stability results of periodic standing waves for the cubic-quintic nonlinear Schrödinger equation. We use implicit function theorem to construct a smooth curve explicit with <i>dnoidal</i> profile such construction can be used that associated period map is strictly increasing in terms energy levels. The monotonicity also useful obtain behaviour non-positive spectrum linearized operator around wave. Concerning stability, dnoidal are orbitally stable space restricted even functions.</p>