Abstract
This paper is devoted to the classification of integrable Davey–Stewartson type equations. A novel approach based on the requirement that such systems must be generated by a polynomial dispersionless Lax pair is used to obtain a list of potentially deformable dispersionless systems. Integrable dispersive systems and their Lax pairs are then constructed by employing a perturbative algorithm using the method of hydrodynamic reductions. Some of the found systems seem to be new.
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