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The existence of contact transformations for evolution-type equations. (English) Zbl 0945.35006
The authors consider $$n$$th order evolution equations $$u_t = F(t,x,u,u_x,u_{xx},\dots,u_{(n)})$$ and give an elementary proof that their contact transformations are exhausted by extended Lie transformations if $$F$$ is expandable as a power series in terms of the derivatives $$u_{xx},\dots,u_{(n)}$$.

##### MSC:
 35A30 Geometric theory, characteristics, transformations in context of PDEs 35A22 Transform methods (e.g., integral transforms) applied to PDEs 35G25 Initial value problems for nonlinear higher-order PDEs
##### Keywords:
extended Lie transformations
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