Authors: Paul Kersten, I. Krasil`shchik, A. Verbovetsky
We discuss the dispersionless Boussinesq type equation, which is
equivalent to the Benney-Lax equation, being a system of equations
of hydrodynamical type. The results include: a description of local and
nonlocal Hamiltonian and symplectic structures, hierarchies of
symmetries, hierarchies of conservation laws, recursion operators
for symmetries and generating functions of conservation laws
(cosymmetries). Highly interesting are the appearances of operators
that send conservation laws and symmetries to each other but are
neither Hamiltonian, nor symplectic. These operators give rise to a
noncommutative infinite-dimensional algebra of recursion operators.
37 pages, LaTeX-2e.
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