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In this paper, we establish orbital stability results of cnoidal periodicwaves for the cubic nonlinear Klein-Gordon and Schr\"odinger equations. Thespectral analysis for the corresponding linearized operator is established byusing the Floquet theory and a Morse Index Theorem. First, we prove that thecnoidal waves for the cubic Klein-Gordon equation are orbitally unstable as adirect application of Grillakis, Shatah and Strauss' theory. The orbitalstability of cnoidal waves for the Schr\"odinger equation is established byconstructing a suitable Lyapunov functional restricted to the associated zeromean energy space.

Cnoidal Waves for the cubic nonlinear Klein-Gordon and Schr\"odinger Equations