title: Growing-and-decaying mode solution to the Davey-Stewartson equation.
abstract: The growing-and-decaying mode solution to the Davey-Stewartson equation are presented, which describe the long time evolution of the Benjamin-Feir unstable mode in two dimensions. A solution consisting of a line soliton and a growing-and-decaying mode shows that the Benjamin-Feir unstable mode does not destroy the structure of the line soliton. The breather solution and rational growing-and-decaying mode solution are also presented.
authors.affiliation: Department of Mathematical Sciences, College of Engineering, Osaka Prefecture University, Sakai, Osaka 599-8531, Japan.
authors.forename: M
authors.initials: M
authors.lastname: Tajiri
authors.forename: T
authors.initials: T
authors.lastname: Arai