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We show that the Ginzburg-Landau expansion of the grand potential for theBogoliubov-de Gennes Hamiltonian is determined by the integrable nonlinearequations of the AKNS hierarchy, and that this provides the naturalmathematical framework for a hidden nonlinear quantum mechanical supersymmetryunderlying the dynamics.

The Bogoliubov/de Gennes system, the AKNS hierarchy, and nonlinear quantum mechanical supersymmetry