  We investigate the analyticity of the attractors of a class of
Kuramoto-Sivashinsky type pseudo-differential equations in higher dimensions,
which are periodic in all spatial variables and possess a universal attractor.
This is done by fine-tuning the techniques used in a previous work of the
second author, which are based on an analytic extensibility criterion involving
the growth of $\nabla^n u$, as $n$ tends to infinity (here $u$ is the
solution). These techniques can now be utilised in a variety of higher
dimensional equations possessing universal attractors, including
Topper--Kawahara equation, Frenkel--Indireshkumar equations and their
dispersively modified analogs. We prove that the solutions are analytic
whenever $\gamma$, the order of dissipation of the pseudo-differential
operator, is higher than one. We believe that this estimate is optimal, based
on numerical evidence.
