Abstract
The N=2 superfield form of the classical N=2 super W 3 algebra recently obtained in terms of N=1 superfields from a supersymmetric Gelfand-Dikki construction is presented. This more economical description makes it feasible to study the integrable equations with this algebra as Hamiltonian structure providing N=2 supersymmetric analogues of the Boussinesq equation. Evidence for the existence of three such equations is presented, the same number as the number of N=2 supersymmetric KdV equations.
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