A modulational stability analysis is presented for real, two‐phase sine‐Gordon wavetrains. Using recent results on the geometry of these real solutions, an invariant representation in terms of Abelian differentials is derived for the sine‐Gordon modulation equations. The theory thus attains the same integrable features of the previously completed KdV and sinh‐Gordon modulations. The twophase results are as follows: kink‐kink trains are stable, while the breather trains and kink‐radiation trains are unstable, to
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