Aa. Alexeyev, THE PAINLEVE APPROACH FOR PERTURBED NONLINEAR EQUATIONS - BACKLUND-TYPE AND MIURA-TYPE TRANSFORMATIONS, Journal of physics. A, mathematical and general, 28(6), 1995, pp. 1699-1712
A modification of the singular manifold or WTC method is proposed for
perturbed nonlinear PDEs and its application is illustrated with sever
al examples. As a result, approximate auto-Backlund and Miura-type tra
nsformations are constructed for the equations under consideration.