Discrete spectra and dampes waves in quasilinear theory†

The consequences of the quasilinear equations are explored. Particular attention is paid to the differences between the one-dimensional and the two- and three-dimensional cases, and to the differences between the cases of discrete and continuous wave-number spectra. The possibilities of and problems associated with including damped waves are treated. The relation between conservation laws and the ‘resonance approximation’, in which the limit of zero growth rate for the unstable waves is taken at finite times, is clarified. Numerical solutions for the one-dimensional case with finite growth rate are presented.