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We predict a new class of excitations propagating along a Josephson vortex intwo-dimensional Josephson junctions. These excitations are associated with thedistortion of a Josephson vortex line and have an analogy with shear waves insolid mechanics. Their shapes can have an arbitrary profile, which is retainedwhen propagating. We derive a universal analytical expression for the energy ofarbitrary shape excitations, investigate their influence on the dynamics of avortex line, and discuss conditions where such excitations can be created.Finally, we show that such excitations play the role of a clock for arelativistically-moving Josephson vortex and suggest an experiment to measure atime dilation effect analogous to that in special relativity.

Shape waves in 2D Josephson junctions: exact solutions and time dilation