Asynchronous Development of the Growing-and-Decaying Mode

The solution to the Davey–Stewartson I equation is analyzed to show that the resonance between periodic soliton and growing-and-decaying mode exists. Under the quasi-resonant condition, the mode develops first in the one side region of the periodic soliton. The periodic soliton is accelerated as a result of the growth and decay of the mode existed in the region and the wave field shifts to the intermediate state, where only the periodic soliton exists. This intermediate state persists over a comparatively long time interval. After sufficiently long time, the mode starts to grow in the opposite side of the periodic soliton.