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Wide classes of nonlinear mathematical physics equations are described thatadmit order reduction through the use of the von Mises transformation, with theunknown function taken as the new independent variable and an appropriatepartial derivative taken as the new dependent variable. RF-pairs and associatedB\"acklund transformations are constructed for evolution equations of generalform (special cases of which are Burgers, Korteweg--de Vries, and Harry Dymtype equations as well as many other nonlinear equations of mathematicalphysics). The results obtained are used for order reduction and constructingexact solutions of hydrodynamics equations. A generalized Calogero equation anda number of other new integrable nonlinear equations are considered.

The von Mises transformation: order reduction and construction of Backlund transformations and new integrable equations