Landau-Ginzburg Lagrangians of minimal W-models with an integrable perturbation

We construct Landau-Ginzburg Lagrangians for minimal bosonic (N = 0) W-models perturbed with the least relevant neutral field, inspired by the theory of N = 2 supersymmetric Landau-Ginzburg Lagrangians. They agree with the Lagrangians for the unperturbed models previously found with Zamolodchikov's method and describe the phase transition between regimes III and IV of the Jimbo et al. IRF models. We briefly study their properties, e.g. the perturbation algebra and the soliton structure, We conclude that the known properties of N = 2 solitons (BPS, etc.) hold as well. Hence, a connection with the generalized supersymmetric structure of minimal W-models is conjectured.