Higgs Pair-Production in the Standard Model at Next Generation Linear $e^+e^-$ Colliders

We study the Higgs pair-production in the Standard Model of the strong and electroweak interactions at future $e^{+}e^{-}$ collider energies, with the reaction $e^{+}e^{-}to t bar t HH$. We evaluated the total cross section of $tbar tHH$ and calculate the number total of events considering the complete set of Feynman diagrams at tree-level. The numerical computation is done for the energy which is expected to be available at a possible Next Linear $e^{+}e^{-}$ Collider: with center-of-mass energy $800, 1600$ $GeV$ and luminosity 1000 $fb^{-1}$.