We investigate nonlinear resonant modes in coupled sine-Gordon systems with open boundary conditions. The system models coupled Josephson junctions with boundary conditions representing the situation where an external magnetic field is applied. The so-called Fiske modes are found to exist in phase-locked states where the equivalent voltages across the individual coupled Josephson junctions are either identical or identical with opposite signs. The analysis covers all Fiske modes including the

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... ux-flow region. We present a comprehensive comparison between results on analytical treatment and direct numerical simulations of the coupled field equations.