Breathers in the one-dimensional roll structure of twisted nematics

The dynamics of nonsingular defects has been studied experimentally and theoretically in the periodic roll structures arising at electroconvection in nematic liquid crystals twisted by $\pi/2$. The presence of an axial component of the velocity of the hydrodynamic flow with the opposite direction in the neighboring rolls is characteristic of roll structures in twisted nematics. The quantitative estimates of the critical frequency of the oscillations of structural defects have been obtained on the basis of the nonlinear equation of motion for the roll displacement. It has been found that the periodic creation and annihilation of a pair of edge dislocations with the topological indices $+1$ and $-1$ occur in the process of oscillations of a defect with a nonsingular nucleus. It has been demonstrated that oscillating defects with zero topological indices correspond to the solution of the sine-Gordon equation in the form of standing breathers.