Summary
We describe the finite-gap solutions of different modifications of the Davey-Stewartson (DS) equations. The restrictions on the spectral data which give us solutions of the real forms DS1 and DS2+ of DS are the same as those in the case of KP1 and KP2 of the Kadomtsev-Petviashvily equation. But for DS2− the restrictions that we regard have no analogues in other integrable systems. We describe also the restrictions that provide regularity of those solutions for DS1 and DS2±. The finite-gap solutions include rational and soliton solutions. We give some classes of those solutions. The well-known dromions for DS1 are examples of that kind.
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Malanyuk, T.M. Finite-gap solutions of the Davey-Stewartson equations. J Nonlinear Sci 4, 1–21 (1994). https://doi.org/10.1007/BF02430624
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DOI: https://doi.org/10.1007/BF02430624