title: Resonant interaction of modulational instability with a periodic soliton in the Davey-Stewartson equation.
abstract: The time evolution of the Benjamin-Feir unstable mode in two dimensions is studied analytically when it resonates with a periodic soliton. The condition for resonance is obtained from an exact solution to the hyperbolic Davey-Stewartson equation. It is shown that a growing-and-decaying mode exists only in the backward (or forward) region of propagation of the periodic soliton if the resonant condition is exactly satisfied. Under a quasiresonant condition, the mode grows at first on one side from the periodic soliton, but decays with time. The wave field shifts to an intermediate state, where only a periodic soliton in a resonant state appears. This intermediate state persists over a comparatively long time interval. Subsequently, the mode begins to grow on the other side from the periodic soliton.
authors.affiliation: Department of Mathematical Sciences, Graduate School of Engineering, Osaka Prefecture University, Sakai, Japan.
authors.forename: Masayoshi
authors.initials: M
authors.lastname: Tajiri
authors.forename: Hiroyuki
authors.initials: H
authors.lastname: Miura
authors.forename: Takahito
authors.initials: T
authors.lastname: Arai