Traveling edge states in massive Dirac equations along slowly varying edges

Abstract Topologically protected wave motion has attracted considerable research interest due to its chirality and potential applications in many applied fields. We construct quasi-traveling solutions the 2D Dirac equation with a domain wall mass this work. It is known that system admits exact explicit traveling solutions, which are termed edge states if interface straight line. By modifying such we quasi-traveling-wave nearly straight. The approximate two scenarios given. One circular large radius, second line slowly varying along perpendicular direction. show valid long lifespan by energy estimates. Numerical simulations provided support our analysis both qualitatively quantitatively.