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A supersymmetric breaking procedure for $N=1$ Super KdV, using a Cliffordalgebra, is implemented. Dirac's method for the determination of constraints isused to obtain the Hamiltonian structure, via a Lagrangian, for the resultingsolitonic system of coupled Korteweg-de Vries type system. It is shown that theHamiltonian obtained by this procedure is bounded from below and in that senserepresents a model which is physically admissible.

The Hamiltonian structure of a coupled system derived from a supersymmetric breaking of Super KdV equations