Abstract:
Nonlinear equations of the form
$$
\frac{\partial u}{\partial t}=\frac{\partial^n{u}}{\partial x^n}+F\biggl(x,u,\dots,\frac{\partial^{n-1}u}{\partial x^{n-1}}\biggr),\quad n\geqslant 2,
$$
are constructed; they are associated with linear substitutions of the Cole–Hopf type
and have an infinite set of local symmetries. For $n\leqslant 5$, these equations together
with equations of Korteweg–de Vries type exhaust the list of equations of the given
type possessing an infinite set of local symmetries.
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