Osaka Preefecrure University
Ohno-Dai 7-17-7, Osaka Sayama, Osaka 589-0023 Japan
E-mail: tajiri@nm.ms.osakafu-u.ac.jp

On asynchronous development of the growing-and-decaying mode

Abstract:
The solutions to the Davey-Stewartson equation are analyzed to show that the resonances between line soliton and growing-and-decaying mode and periodic soliton and growing-and-decaying mode exist.  If the resonant condition is exactly satisfied, the growing-and-decaying mode exists only in the forward region of propagation of line soliton (or periodic soliton) and the line soliton (or periodic soliton) is accelerated.  Under the quasi-resonant condition, the mode develops first in the forward region of propagation of the line soliton (or periodic soliton).  The line soliton (or periodic soliton) is accelarated as a result of the grow and decay of the mode existed in the forward region and the wave field shifts to the intermediate sate, where the only line soliton (or periodic soliton) exists.  This intermediate state persists over a comparatively long time interval.  After sufficient long time, the mode starts to grow in the opposite site of the line soliton (or periodic soliton).  The existence of solitons changes the evolution of the growing-and-decaying mode drastically as if the solitons dominated the evolution of the instability in whole region of the wave field.