Sizable triple Higgs couplings in the 2HDM: Prospects for future $e^+e^-$ colliders

In the framework of the $mathcal{CP}$ conserving Two Higgs Doublet Model (2HDM), type I and II, we study the triple Higgs couplings with at least one light $h$ Higgs boson that is identified by the 125 GeV Higgs boson. We define benchmark planes that exhibit large values of triple Higgs couplings, while being in agreement with all experimental and theoretical constraints. Finally, we analyze the impact of the triple Higgs couplings on the production cross section of two neutral Higgs bosons in two channels, $sigma(e^+e^-to h_i h_j Z)$ and $sigma(e^+e^- to h_i h_j ubar{ u})$ with $h_i h_j = hh, hH, HH, AA$. We show that the triple Higgs couplings have an important impact on these $e^+e^-$ production cross sections.