Conformal invariance and integrable models

Abstract

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 interesting results. In this paper, we will focus mainly in obtaining new symmetries and new integrable models. Starting from the conformal invariance of an integrable model, one can obtain infinitely many non-local symmetries. Many types of (1 + 1)- and (2 + 1)-dimensional new sine - Gordon (or sinh - Gordon) extensions are obtained from the conformal flow equations of the Koerteweg - de Vries type equations. Many other kinds of integrable models can be obtained from the conformal constraints of the known integrable models.