Analogs of the Burgers equation of arbitrary order
Nonlinear equations of the form \[ \partial u/\partial t=\partial^ nu/\partial x^ n+F(x,u,\partial^{n-1}u/\partial x^{n-1}),\quad n\geq 2, \] are constructed; they are associated with linear substitutions of the Cole-Hopf type and have an infinite set of local symmetries. For \(n\leq 5\), 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.
scientific article; zbMATH DE number 3977554