  The Kuramoto model provides a prototypical framework to synchronization
phenomena in interacting particle systems. Apart from full phase synchrony
where all oscillators behave identically, identical Kuramoto oscillators with
ring-like nonlocal coupling can exhibit more elaborate patterns such as
uniformly twisted states. It was discovered by Wiley, Strogatz and Girvan in
2006 that the stability of these twisted states depends on the coupling range
of each oscillator. In this paper, we analyze twisted states and their
bifurcations in the infinite particle limit of ring-like nonlocal coupling. We
not only consider traditional pairwise interactions as in the Kuramoto model
but also demonstrate the effects of higher-order nonpairwise interactions,
which arise naturally in phase reductions. We elucidate how pairwise and
nonpairwise interactions affect the stability of the twisted states, compute
bifurcating branches, and show that higher-order interactions can stabilize
twisted states that are unstable if the coupling is only pairwise.
