CONFORMAL-INVARIANCE AND INTEGRABLE MODELS

Usually, an integrable nonlinear partial differential equation can be transformed to its conformal invariant form (Schwartz form). Using the conformal invariance of the integrable models, we can obtain many int eresting results. In this paper, we will focus mainly in obtaining new symmetries and new integrable models. Starting from the conformal inv ariance of an integrable model, one can obtain infinitely many non-loc al symmetries. Many types of(1+1)- and (2+1)-dimensional new sine-Gord on (or sinh-Gordon) extensions are obtained from the conformal dow equ ations of the Koerteweg-de Vries type equations. Many other kinds of i ntegrable models can be obtained from the conformal constraints of the known integrable models.