Solutions of the Davey-Stewartson II equation with arbitrary rational localization and nontrivial interaction

Abstract We study a large class of solutions of the Davey-Stewartson II equation obtained with the use of a Wronskian scheme. Unlike the well-known lumps, these solutions have an arbitrary rational localization in the plane and describe typical interactions consisting of head-on collisions with a π 2 scattering angle. We also find the connection between the Wronskian method and the inverse spectral transform formalism associated with the lumps. We finally show that these novel solutions can also be obtained through the method of coalescence of poles.

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