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| We investigate the integrable cases of the elliptic-hyperbolic-hyperbolic (EHH) generalized Davey-Stewartson (GDS) system using the vertex method developed by Zakharov and Shulman. The system we analyze is called the GDS system because it was derived as a 3-component system so as to incorporate the effect of the second spatial coordinate, that was omitted in the derivation of the 2-component Davey-Stewartson (DS) system. Physically meaningful cases of the GDS system comprise the EHH version which we consider in this work. The method produces necessary conditions for the inverse scattering transform to be applied successfully. Implementing this method, we prove that the EHH-GDS system with physical parameters is integrable only when it can be reduced to an integrable, necessarily elliptic-hyperbolic, DS system. |
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