  Topological phases have become an enabling role in exploiting new
applications of nonlinear optics in recent years. Here we theoretically propose
a valley photonic crystal resonator emulating topologically protected
dissipative Kerr soliton combs. It is shown that topological resonator modes
can be observed in the resonator. Moreover, we also simulate the dynamic
evolution of the topological resonator with the injection of a continuous-wave
pump laser. We find that the topological optical frequency combs evolve from
Turing rolls to chaotic states, and eventually into single soliton states. More
importantly, such dissipative Kerr soliton combs generated in the resonator are
inborn topologically protected, showing robustness against sharp bends and
structural disorders. Our design supporting topologically protected dissipative
Kerr soliton combs could be implemented experimentally in on-chip
nanofabricated photonic devices.
