Breather annihilation by simple dissipation

A numerical experiment is conducted on the decay of a sine-Gordon breather under simple dissipation. Both the spatial configuration and the (nonlinear) spectral configurations are measured numerically. The spectral configuration establishes that the breather is annihilated in finite time and that the annihilation process is accomplished by the generation of a long-wavelength packet of dispersive radiation. The nonlinear radiation density, which is measured numerically, is seen to be order 1 and is extremely well approximated by a sech profile in $k$ space. Finally, a representation of the spectral configuration by "resonance" states is investigated.