Self-interaction of Alfvén waves in a cylindrical waveguide filled with an ideally conducting compressible plasma

The nonlinear behaviour of azimuthally symmetric Alfvén waves propagating along the axis of a cylindrical ideally conducting compressible fluid-filled waveguide is investigated. It is shown that the nonlinear evolution of such waves is governed by the nonlinear Schrödinger equation. Modulational instability for fundamental (m = 1) radial mode is discussed for α² = 0·1,0·2, 0·3 and different values of k. The amplitude-dependent frequency and wavenumber shifts are calculated and their variations with wavenumber are shown graphically.