  One of the main objectives of almost all future (lepton) colliders is to
measure the self-coupling of triple Higgs in the Standard Model. By elongating
the Standard Model's scalar sector, using incipient Higgs doublet along with a
quadratic (Higgs) potential should reveal many incipient features of the model
and the possibility of the emergence of additional Higgs self-couplings. The
self-coupling of the Higgs boson helps in reconstructing the scalar potential.
The main objective of this paper is to extract Higgs self-coupling by
numerically analyzing several scattering processes governed by two Higgs
doublet models (2HDM). These scattering processes include various possible
combinations of final states in the triple Higgs sector. The determination of
production cross-section of scattering processes is carried out using two
different scenarios, with and without polarization of incoming beam and is
extended to a center of mass energy up to $\sqrt{s}$ = 3 $TeV$. The computation
is carried out in Type-1 2HDM. Here we consider the case of exact alignment
limit ($s_{\beta \alpha}$ = 1) and masses of extra Higgs state are equal that
is $m_H = m_{H^0} = m_{A^0} = m_{H^\pm}$. This choice is made to minimize the
oblique parameters. The decays of the final state of each process are
investigated to estimate the number of events at integrated luminosity of
$1ab^{-1}$ and $3ab^{-1}$.
