A derivation of the Lorenz equations for some unstable dispersive physical systems

The amplitude equations which are valid in the neighbourhood of the bifurcation point of a class of dispersively unstable physical systems when small dissipation is included are shown to be transformable to the Lorenz equations. There is a strong connection with systems which yield equations solvable by the inverse scattering transform when damping is excluded and spatial variation included. Two examples are given in very brief detail: (1) a two-layer model for baroclinic instability, (2) the laser equations giving rise to the SIT equations.