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

We show that the Ginzburg–Landau expansion of the grand potential for the Bogoliubov–de Gennes Hamiltonian is determined by the integrable nonlinear equations of the AKNS hierarchy, and that this provides the natural mathematical framework for a hidden nonlinear quantum mechanical supersymmetry underlying the dynamics.