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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
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