Invertible changes of variables generated by Bäcklund transformations

In the classification of partial differential equations, one cannot avoid the use of invertible changes of variables, which include not only the long-known point and contact transformations but also, for example, so-called symmetric and generalized contact transformations (reviewed by Mikhailov, Shabat, and Yamilov [1]). The present paper considers a further class of invertible changes of variables.