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Topologically protected wave motion has attracted considerable interest dueto its novel properties and potential applications in many different fields. Inthis work, we study edge modes and traveling edge states via the linear Diracequations with so-called domain wall masses. The unidirectional edge stateprovides a heuristic approach to more general traveling edge states through thelocalized behavior along slowly varying edges. We show the leading asymptoticsolutions of two typical edge states that follow the circular and curved edgeswith small curvature by analytic and quantitative arguments.

Traveling edge states in massive Dirac equations along slowly varying edges