Propagating wave patterns and "peakons" of the Davey-Stewartson system

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Abstract

Two exact, doubly periodic, propagating wave patterns of the Davey-Stewartson system are computed analytically by a special separation of variables procedure. For the first solution there is a cluster of smaller peaks within each period. The second one consists of a rectangular array of 'plates' joined together by sharp edges, and is thus a kind of 'peakons' for this system of (2 + 1) (2 spatial and 1 temporal) dimensional evolution equations. A long wave limit will yield exponentially localized waves different from the conventional dromion. The stability properties and nonlinear dynamics must await further investigations. © 2005 Elsevier Ltd. All rights reserved.

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Chow, K. W., & Lou, S. Y. (2006). Propagating wave patterns and “peakons” of the Davey-Stewartson system. Chaos, Solitons and Fractals, 27(2), 561–567. https://doi.org/10.1016/j.chaos.2005.04.036

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