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To establish the Higgs mechanism sui generis experimentally, the self-energypotential of the Higgs field must be reconstructed. This task requires themeasurement of the trilinear and quadrilinear self-couplings, as predicted, forinstance, in the Standard Model or in supersymmetric theories. The couplingscan be probed in multiple Higgs production at high-luminosity e^+e^- linearcolliders. Complementing earlier studies to develop a coherent picture of thetrilinear couplings, we have analyzed the production of pairs of neutral Higgsbosons in all relevant channels of double Higgs-strahlung, associated multipleHiggs production and WW/ZZ fusion to Higgs pairs.

Testing Higgs self-couplings at $e^+e^-$ linear colliders