  The Poisson structure of a coupled system arising from a supersymmetric
breaking of N=1 Super KdV equations is obtained. The supersymmetric breaking is
implemented by introducing a Clifford algebra instead of a Grassmann algebra.
The Poisson structure follows from the Dirac brackets obtained by the
constraint analysis of the hamiltonian of the system. The coupled system has
multisolitonic solutions. We show that the one soliton solutions are Liapunov
stable.
