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- W1994114994 abstract "We solve an initial-boundary value problem for the Davey-Stewartson 1 equation, which is a two-dimensional generalization of the nonlinear Schrödinger equation. This equation, which describes the interaction of a surface wave envelope of amplitude q(x, y, t) with the mean flow, arises in a wide range of physical problems. We find that the energy from the mean flow can be transferred to the surface envelope and create focusing effects. Indeed, for generic non-zero boundary conditions on the mean flow, an arbitrary initial q(x, y, t) will form a number of two-dimensional, exponentially decaying in both x and y, localized structures. Furthermore, in contrast to the one-dimensional solitons, these solutions do not preserve their form upon interaction and hence can exchange energy. These coherent structures can be driven everywhere in the plane by choosing a suitable motion for the boundaries. We call these novel localized coherent structures dromions." @default.
- W1994114994 created "2016-06-24" @default.
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- W1994114994 date "1990-08-01" @default.
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- W1994114994 title "Dromions and a boundary value problem for the Davey-Stewartson 1 equation" @default.
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- W1994114994 doi "https://doi.org/10.1016/0167-2789(90)90050-y" @default.
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