Abstract
The method of third order mode coupling is applied to a general evolution equation, which includes as special cases many of the modified and higher order Koreteweg de Vries equations which have recently appeared in the literature. The equations for the slow changes in the amplitudes and phases are derived and specialised to two different classes of evolution equations. The first class exhibits the property of nonresonant mode decoupling, the evolution of each wave being governed only by its own parameters. Included in this class are the KdV equation, some of the mKdV equations and the Sharma-Tasso-Olver equation. Equations of the second class leave the amplitudes and hence the energetics of the waves constant as long as the mode coupling is non-resonant. Here one finds the fifth-order KdV equations, besides the KdV and STO equations.