A Flow for the Seiberg-Witten Equations

Question

I propose to define a flow for the Seiberg-Witten equations:

$\frac{\partial \psi}{\partial t}= D_A \psi$

$i <\frac{\partial A}{\partial t}(X)Y. \psi,\psi>-i<\frac{\partial A}{\partial t}(Y)X.\psi,\psi>=F(A)_++\omega (\psi)/4$

The flow is invariant under the gauge group. The fixed points are the solutions of the Seiberg-Witten equations.

Is this flow an integrable system?