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We study the self-modulation of a circularly polarized Alfv\'en wave in a strongly magnetized relativistic electron-positron plasma with finite temperature. This nonlinear wave corresponds to an exact solution of the equations, with a dispersion relation that has two branches. For a large magnetic field, the Alfv\'en branch has two different zones, which we call the normal dispersion zone (where $d\ensuremath{\omega}/dkg0$) and the anomalous dispersion zone (where $d\ensuremath{\omega}/dkl0$). A nonlinear Schr\"odinger equation is derived in the normal dispersion zone of the Alfv\'en wave, where the wave envelope can evolve as a periodic wave train or as a solitary wave, depending on the initial condition. The maximum growth rate of the modulational instability decreases as the temperature is increased. We also study the Alfv\'en wave propagation in the anomalous dispersion zone, where a nonlinear wave equation is obtained. However, in this zone the wave envelope can evolve only as a periodic wave train.

Thin fluid films can have surprising behavior depending on the boundary conditions enforced, the energy input and the specific Reynolds number of the fluid motion. Here we study the equations of motion for a thin fluid film with a free boundary and its other interface in contact with a solid wall. Although shear dissipation increases for thinner layers and the motion can generally be described in the limit as viscous, inertial modes can always be excited for a sufficiently high input of energy. We derive the minimal set of equations containing inertial effects in this strongly dissipative regime.