The N = 2 supersymmetric generalization of the complex sine-gordon model

A two-dimensional field theoretical model endowed with a Lax pair and invariant under complex supersymmetry is written in a manifestly invariant formulation. The bosonic limit of the model reproduces the complex sine-Gordon equations [that is the reduced O(4) σ-model introduced by Pohlmeyer, Lund-Regge and Getmanov]. The supersymmetry algebra contains central charges which generalize the one found by Witten and Olive in the super sine-Gordon case.