Department of Higher Mathematics,

Ivanovo State Power University,

34 Rabfakovskaya Str.,

153003 Ivanovo,

RUSSIA

E-mail: arthemy@mccme.ru, kiselev@math.ispu.ru

**New recursive chains of N=1 homogeneous superequations**

**Abstract:**

New examples of *N*=1 homogeneous superequations that precede
the translation symmetry with respect to the (super)recursion operators
are described. The Abelian (super) coverings over the initial *N*=1
systems are reconstructed and weighted (non)local recursion operators as
well as the Hamiltonian structures are obtained. Reduction of one system
to a super-Burgers equation is performed. An example of Hamiltonian hierarchy
whose elements are of growing weights and constant differential order 3/2
is discovered.

Joint work with Professor *Thomas
WOLF*.