Oleksandr A. Pocheketa (Institute of Mathematics of the NAS of Ukraine, Kyiv)

Equivalence groupoid of a class of generalized potential Burgers equations

Abstract:

Consider admissible transformations that constitute the equivalence groupoid of a class of $(1+1)$-dimensional second-order evolution equations $$v_{t}+v_{x}^2+f(t,x)v_{xx}=0, \quad f\ne0. $$ This class is related via potentialization with two classes of variable-coefficient generalized Burgers equations. Its equivalence groupoid is described via partitioning the entire class into three normalized subclasses such that there are no point transformations between equations from different subclasses. For each of these subclasses its equivalence group of an appropriate kind is constructed.