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Symmetries of variable coefficient Korteweg-de Vries equations. (English) Zbl 0767.35077
Summary: The Lie point symmetries of the equation $u\sb t+f(x,t)uu\sb x+g(x,t)u\sb{xxx}=0$ are studied. The symmetry group is shown to be, at most, four dimensional, and this occurs if and only if the equation is equivalent, under local point transformations, to the KdV equation with $f=g=1$. For nine different classes of functions $f$ and $g$, the symmetry group turns out to be three dimensional. Two-dimensional and one-dimensional symmetry groups occur for 11 and 15 classes of equations, respectively.

##### MSC:
 35Q53 KdV-like (Korteweg-de Vries) equations 35A30 Geometric theory for PDE, characteristics, transformations 37J35 Completely integrable systems, topological structure of phase space, integration methods 37K10 Completely integrable systems, integrability tests, bi-Hamiltonian structures, hierarchies
##### Keywords:
Lie point symmetries; symmetry groups
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