We construct linear bases of free Gelfand-Dorfman-Novikov (GDN) superalgebras. As applications, we prove a Poincare-Birkhoff-Witt (PBW) type theorem, that is, every GDN superalgebra can be embedded into its universal enveloping associative differential supercommuative algebra. An Engel theorem is given.
- GDN superalgebra
- Poincaré-Birkhoff-Witt theorem
- Poincare-Birkhoff-Witt theorem
- HYDRODYNAMIC TYPE