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Analytic solutions for excitations in the anisotropic, multilayered high-Tc superconductor of the Bi2Sr2CaCu2Ox-type are discussed. Understanding such excitations is important as a diagnostic tool for the experimental investigation of intrinsic materials properties, as well as being a basis for making devices. The linear plasma resonance is derived theoretically using the inductive coupling model. The eigenmodes of the plasma oscillation are discussed analytically. Further analysis is based on the plasma dispersion relation and the properties of lightly damped Josephson vortices known to exist in these layered superconductors. It is shown that symmetries from the plasma dispersion relation and the dynamic properties of the vortices are closely connected. This can be used to predict fluxon behaviour even in the absence of fluxon analytic solutions. The model assumes that vortices and an applied magnetic field are parallel to the planes. A semi-analytic derivation of a non-linear parametric excitation of certain of the plasma modes in Bi2Sr2CaCu2Ox single crystals is mentioned.