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.
Sundermeyer,Constrained dynamics with applications to Yang-Mills theory, general relativity, classical spin, dual string model(Springer-Verlag, 1982)
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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.