Fluxon modes in stacked Josephson junctions: The role of linear modes

Plasma modes in stacked Josephson junctions are easily understood analytically from a linearization of the coupled sine-Gordon equation describing the system. We demonstrate here by numerical methods that the analytically derived symmetries of the plasma modes are carried over to the fluxon modes. Using this fact we are, with a few exceptions, able to predict and construct a full family of Josephson fluxon modes without using numerical methods. The nature of the locking mechanism needed to create the technologically important in-phase fluxon modes is discussed.