Oscillatory Solitary Waves in Dispersive Media

Abstract

Steady solutions of a generalized Korteweg-de Vries equation which has an additional fifth order derivative term are investigated on the basis of a numerical calculation. It is found that either compressive or rarefactive solitary waves are possible to exist according as the dispersion is negative or positive and that the solitary waves take the oscillatory structure when the coefficient of the fifth order derivative term dominates over that of the third order one.