Asymptotic development of finite amplitude cylindrical ion acoustic waves

It is observed experimentally that a fine amplitude cylindrical ion acoustic wave develops at large distances from the exciter an oscillatory structure which resembles an Airy function but its amplitude oscillations are asymmetric. This phenomenon can be described by solutions of the linearized Korteweg-de Vries equation in self-similar variables. This equation has been solved by others for integral values of a certain parameter γ. New solutions which can be represented as the Weyl transform of the Airy function are obtained for fractional values of γ. These solutions are similar to the observed waveform. The measured rate of spatial damping of the oscillations and the variation of their period with respect to distance and Debye length agree well with those predicted by these solutions. (author)