  In this paper we show that the homeomorphic solutions to each nonlinear
Beltrami equation $\partial_{\bar{z}} f = \mathcal{H}(z, \partial_{z} f)$
generate a two-dimensional manifold of quasiconformal mappings
$\mathcal{F}_{\mathcal{H}} \subset W^{1,2}_{\mathrm{loc}}(\mathbb{C})$.
Moreover, we show that under regularity assumptions on $\mathcal{H}$, the
manifold $\mathcal{F}_{\mathcal{H}}$ defines the structure function
$\mathcal{H}$ uniquely.
