Evolution equation for infinitesimal rotational discontinuities

Abstract

An evolution equation in the form of a modified Korteweg-de Vries equation is developed which describes the small-amplitude version of the infinitesimal rotational discontinuity (RD) studied by Wang and Sonnerup (1984). It is shown that the small-amplitude version of the equilibrium pulse solution obtained by Wang and Sonnerup is metastable and thus unlikely to arise spontaneously. When the initial pulse amplitude is smaller than and/or the initial pulse width is greater than the equilibrium value, the pulse decays. When the reverse is the case, the pulse is converted to an infinitesimal intermediate-mode solitary wave having greater pulse amplitude and speed. A simulation experiment is performed in which one of the equilibrium intermediate-mode solitary waves overtakes another, less rapidly moving version of the same wave. The existence of multipeaked intermediate-mode solitary pulses is demonstrated.