, Volume 4, Issue 1, pp 1-21

Finite-gap solutions of the Davey-Stewartson equations

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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.

Communicated by Thanasis Fokas