  We study integrable deformations of two-dimensional non-linear sigma-models
and present a new class of classical solutions to critical bi-Yang-Baxter
models for general groups. For the simplest example, namely the SL(2,R)
bi-Yang-Baxter model, we show that our solutions can be mapped to the known
complex uniton solutions of the SU(2) bi-Yang-Baxter model. In general, our
solutions are constructed from so-called Sl(2)-orbits that play a central role
in the study of asymptotic Hodge theory. This provides further evidence for a
close relation between integrable non-linear sigma-models and the mathematical
principles underlying Hodge theory. We have also included a basic introduction
to the relevant aspects of asymptotic Hodge theory and have provided some
simple examples.
