The nonlinear propagation of plasma waves along a bounded plasma cylin
der is considered, Exact surface and volume wave structures in the rad
ial and azimuthal directions are included, It is shown that in the sma
ll-amplitude limit, mode-mode interactions are described by equations
of the Mathieu type, and the space-time evolution of axially propagati
ng waves is governed by a nonlinear Schrodinger equation.