Geodesic
Equations invariant under differential substitutions
Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 2, pp. 193-200

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The classification of differential autosubstitutions of the form $\hat u=G(u_x,u)$ that are allowed by general evolution equations with one spatial variable is considered. In the one-field case, every such substitution can be reduced to the autosubstitution $\hat u=u+u_x/u$ for the Burgers equation by a point transformation. This substitution is generalized to the two-field case. 
@article{TMF_1998_116_2_a2,
     author = {V. S. Novikov},
     title = {Equations invariant under differential substitutions},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {193--200},
     publisher = {mathdoc},
     volume = {116},
     number = {2},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a2/}
}
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V. S. Novikov. Equations invariant under differential substitutions. Teoretičeskaâ i matematičeskaâ fizika, Tome 116 (1998) no. 2, pp. 193-200. http://geodesic.mathdoc.fr/item/TMF_1998_116_2_a2/