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The Poisson structure of a coupled system arising from a supersymmetricbreaking of N=1 Super KdV equations is obtained. The supersymmetric breaking isimplemented by introducing a Clifford algebra instead of a Grassmann algebra.The Poisson structure follows from the Dirac brackets obtained by theconstraint analysis of the hamiltonian of the system. The coupled system hasmultisolitonic solutions. We show that the one soliton solutions are Liapunovstable.

Poisson structure and stability analysis of a coupled system arising from the supersymmetric breaking of Super KdV