  Motivated by their effect on the gravitational wave signal emitted by cosmic
strings, we study the dynamics of kinks on strings of different tensions
meeting at junctions. The propagation of a kink through a Y-junction leads to
the formation of three `daughter' kinks. Assuming a uniform distribution of the
incoming wave vectors at the junction, we find there is a significant region of
configuration space in which the sharpness of at least one of the daughter
kinks is enhanced relative to the sharpness of the initial kink. For closed
loops with junctions we show this leads to an exponential growth in time of
very sharp kinks. Using numerical simulations of realistic, evolving cosmic
string loops with junctions to calculate the distribution of kink amplitudes as
a function of time, we show that loops of this kind typically develop several
orders of magnitude of very sharp kinks before the two junctions collide. This
collision, or other effects such as gravitational backreaction, may end the
proliferation.
