Abstract
In this paper, the method of multiple-scales is used to investigate the weak nonlinear self-modulation of the gravity-surface tension standing wave mode in a finite deep fluid which is filled in a rectangular resonator. The detailed analysis and calculations about the nonpropaga-ting soliton discovered by Wu et al. are made when external driving and damping of the surface wave are considered. The nonpropagating soliton theory established by Larraza, Put-terman and Miles is revised and developed. The correct second harmonic resonace condition about gravity-surface tension wave in the rectangular trough is obtained. The stabilities of propagating soliton are analyzed in detail according to σ-kd diagram. It is found, in addition to the static depth d, that the surface-tension of fluid is an important parameter which may control the formation of nonpropagating soliton. Finally, the nonlinear tuning curves of the surface wave resonator are discussed and compared with experimental results.
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