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The purpose of this article is to investigate relations betweenW-superalgebras and integrable super-Hamiltonian systems. To this end, weintroduce the generalized Drinfel'd-Sokolov (D-S) reduction associated to a Liesuperalgebra $g$ and its even nilpotent element $f$, and we find a newdefinition of the classical affine W-superalgebra $W(g,f,k)$ via the D-Sreduction. 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 systemswith the Poisson vertex algebras theory. A W-superalgebra with certainproperties can be understood as an underlying differential superalgebra of aseries of integrable super-Hamiltonian systems.

Classical affine W-superalgebras via generalized Drinfeld-Sokolov reductions and related integrable systems