  We revisit the Fermi-Pasta-Ulam-Tsingou lattice (FPUT) with quadratic and
cubic nonlinear interactions in the continuous limit by deducing the Gardner
equation. Through the Hirota bilinear method, multi-soliton solutions are
obtained for the Gardner equation. Based on these solutions, we show the
excitation of an interesting class of table-top soliton molecules in the FPUT
lattice through the velocity resonance mechanism. Depending on the condition on
the free parameters, we classify them as dissociated and synthetic type
molecules. The main feature of the table-top soliton molecules is that they do
not exhibit oscillations in the coalescence region. This property ensures that
they are distinct from the soliton molecules, having retrieval force, of the
nonlinear Schr\"odinger family of systems. Further, to study the stability of
the soliton molecule we allow it to interact with a single (or multi)
soliton(s). The asymptotic analysis shows that their structures remain
constant, though the bond length varies, throughout the collision process. In
addition, we consider the FPUT lattice with quadratic nonlinear interaction and
FPUT lattice with cubic nonlinearity as sub-cases and point out the nature of
the soliton molecules for these cases also systematically. We achieve this
based on the interconnections between the solutions of the Gardner, modified
K-dV and K-dV equations. Finally, we simulate the FPUT chain corresponding to
the Gardner equation numerically and verify the existence of all the soliton
structures associated with it. We believe that the present study can be
extended to other integrable and non-integrable systems with applications in
fluid dynamics, Bose-Einstein condensates, nonlinear optics, and plasma
physics.
