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Pseudosymmetries and differential substitutions. (English. Russian original) Zbl 0672.35033

Funct. Anal. Appl. 22, No. 2, 121-129 (1988); translation from Funkts. Anal. Prilozh. 22, No. 2, 47-56 (1988).
The invariance property of the parabolic equation \[ u_ t=F(x,u,u_ 1,...,u_ n),\quad u_ i=\partial^ iu/\partial x^ i \] under an arbitrary one parameter group G of the point transformations \(\tilde x=\phi (x,u)\), \(\tilde u=\psi (x,u)\) guarantees the existence of a differential transformation \(\sigma_ G\) which transforms the equation (1) into an equation \(\tilde u_ t=\Phi (\tilde x,\tilde u,\tilde u_ 1,...,\tilde u_ n).\)
This paper explains which symmetries of the equation (1) correspond to existence of arbitrary differential transformations.
Reviewer: J.Tian

MSC:

35K55 Nonlinear parabolic equations
35A30 Geometric theory, characteristics, transformations in context of PDEs
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