In order to verify the Higgs mechanism experimentally, the Higgs self-couplings have to be probed. These couplings allow the reconstruction of the characteristic Higgs potential responsible for the electroweak symmetry breaking. The couplings are accessible in a variety of multiple Higgs production processes. The theoretical analysis including the most relevant channels for the production of neutral Higgs boson pairs at high-energy and high-luminosity $e^+e^-$ linear colliders will be presented in this note.
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