Title: Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems,
Abstract: The purpose of this article is to investigate relations between
W-superalgebras and integrable super-Hamiltonian systems. To this end, we
introduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Lie
superalgebra $g$ and its even nilpotent element $f$, and we find a new
definition of the classical affine W-superalgebra $W(g,f,k)$ via the D-S
reduction. This new construction allows us to find free generators of
$W(g,f,k)$, as a differential superalgebra, and two independent Lie brackets on
$W(g,f,k)/\partial W(g,f,k).$ Moreover, we describe super-Hamiltonian systems
with the Poisson vertex algebras theory. A W-superalgebra with certain
properties can be understood as an underlying differential superalgebra of a
series of integrable super-Hamiltonian systems.