The supersymmetric KdV equation has a constrained Hamiltonian with a nonlocal density from fermionic consistency conditions, plus a compact superspace form that reproduces the component equations.
Nutku, Canonical formulation of shallow water waves, Journal of Physics A: Mathematical and General16, 4195 (1983)
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Hamiltonian formulation of the supersymmetric KdV equation
The supersymmetric KdV equation has a constrained Hamiltonian with a nonlocal density from fermionic consistency conditions, plus a compact superspace form that reproduces the component equations.