Abstract
The bi-Hamiltonian structure of an integrable dynamical system introduced by Melnikov (1986) is studied. This equation arises as a symmetry constraint of the KP hierarchy via squared eigenfunctions and can be understood as a Boussinesq system with a source. The standard linear and quadratic Poisson brackets associated with the space of pseudo-differential symbols are used to derive two compatible Hamiltonian operators. A bi-Hamiltonian formulation for the Drinfeld-Sokolov system is derived via reduction techniques.
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