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We consider the propagation of sine-Gordon kinks in a planar curved strip asa model of nonlinear wave propagation in curved wave guides. The homogeneousNeumann transverse boundary conditions, in the curvilinear coordinates, allowto assume a homogeneous kink solution. Using a simple collective variableapproach based on the kink coordinate, we show that curved regions act aspotential barriers for the wave and determine the threshold velocity for thekink to cross. The analysis is confirmed by numerical solution of the 2Dsine-Gordon equation.Comment: 8 pages, 4 figures (2 in color

Kink propagation and trapping in a two-dimensional curved Josephson junction