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

. To establish the Higgs mechanism sui generis experimentally, the self-energy potential of the Higgs field must be reconstructed. This task requires the measurement of the trilinear and quadrilinear self-couplings, as predicted, for instance, in the Standard Model or in supersymmetric theories. The couplings can be probed in multiple Higgs production at high-luminosity e^+e^- linear colliders. Complementing earlier studies to develop a coherent picture of the trilinear couplings, we have analyzed the production of pairs of neutral Higgs bosons in all relevant channels of double Higgs-strahlung, associated multiple Higgs production and WW / ZZ fusion to Higgs pairs.