  Optical microcavities supporting exciton-polariton quasi-particles offer one
of the most powerful platforms for investigation of rapidly developing area of
topological photonics in general, and of photonic topological insulators in
particular. Energy bands of the microcavity polariton graphene are readily
controlled by magnetic field and influenced by the spin-orbit coupling effects,
a combination leading to formation of linear unidirectional edge states in
polariton topological insulators as predicted very recently. In this work we
depart from the linear limit of non-interacting polaritons and predict
instabilities of the nonlinear topological edge states resulting in formation
of the localized topological quasi-solitons, which are exceptionally robust and
immune to backscattering wavepackets propagating along the graphene lattice
edge. Our results provide a background for experimental studies of nonlinear
polariton topological insulators and can influence other subareas of photonics
and condensed matter physics, where nonlinearities and spin-orbit effects are
often important and utilized for applications.
