Abelian Lie symmetry algebras of two-dimensional quasilinear evolution
equations
Abstract
We carry out the classification of abelian Lie symmetry algebras of
two-dimensional second-order nondegenerate quasilinear evolution
equations. It is shown that such an equation is linearizable if it
admits an abelian Lie symmetry algebra that is of dimension greater
than or equal to five or of dimension greater than or equal to three
with rank one.
