Title: On free Gelfand--Dorfman--Novikov superalgebras and a PBW type theorem,
Abstract: We construct a linear basis of a free GDN superalgebra over a field of
characteristic $\neq 2$.
As applications, we prove a PBW theorem, that is, any GDN superalgebra can be
embedded into its universal enveloping commutative associative differential
superalgebra. An Engel theorem under some assumptions is given.