  We study the dynamics of a system of $N$ interacting bosons in a disc-shaped
trap, which is realised by an external potential that confines the bosons in
one spatial dimension to a region of order $\varepsilon$. The interaction is
non-negative and scaled in such a way that its scattering length is of order
$(N/\varepsilon)^{-1}$, while its range is proportional to
$(N/\varepsilon)^{-\beta}$ with scaling parameter $\beta\in(0,1]$. We consider
the simultaneous limit $(N,\varepsilon)\to(\infty,0)$ and assume that the
system initially exhibits Bose-Einstein condensation. We prove that
condensation is preserved by the $N$-body dynamics, where the time-evolved
condensate wave function is the solution of a two-dimensional non-linear
equation. The strength of the non-linearity depends on the scaling parameter
$\beta$. For $\beta\in(0,1)$, we obtain a cubic defocusing non-linear
Schr\"odinger equation, while the choice $\beta=1$ yields a Gross-Pitaevskii
equation featuring the scattering length of the interaction. In both cases, the
coupling parameter depends on the confining potential.
