  We numerically study the breathing dynamics induced by collision between
bright solitons in the one-dimensional Bose-Einstein condensates with strong
dipole-dipole interaction. This breathing phenomenon is closely related to the
after-collision short-lived attraction of solitons induced by the dipolar
effect. The initial phase difference of solitons leads to the asymmetric
dynamics after collision, which is manifested on their different breathing
amplitude, breathing frequency, and atom number. We clarify that the asymmetry
of breathing frequency is directly induced by the asymmetric atom number,
rather than initial phase difference. Moreover, the collision between breathing
solitons can produce new after-two-collision breathing solitons, whose
breathing amplitude can be adjusted and reach the maximum (or minimum) when the
peak-peak (or dip-dip) collision happens.
