Decay of solitons in the electroconvective structure of a nematic liquid crystal

Features of the dynamics of topological defects in an electroconvective structure formed in a $\pi/2$-twisted nematic liquid crystal have been studied. The electroconvective structure (Williams domains) is a system of rolls similar to the system of convective cells in thermal convection. Hydrodynamic flows in rolls of the twisted nematic liquid crystal are helicoidal because the axial velocity component existing in addition to the tangential component has opposite directions in the neighboring rolls. This feature is responsible for the formation of stable localized extended objects-linear defects-oriented normally to Williams domains. The continuity condition for a helicoidal flow of an anisotropic liquid in twisted nematic liquid crystals prevents the decay of a linear defect into single dislocations. The length of the linear defect and the number of dislocations in it are controlled by an ac voltage applied to a liquid crystal cell. In contrast to the case of planar orientation, where linear defects decay into single dislocations with increasing applied voltage, zigzag oscillations appear in this case, but the structure of domains remains stationary. The boundaries between zig and zag regions in the core of the linear defect are dislocations with the topological charges $S = +1$ and $-1$. An “elementary” decay of a dislocation with the topological charge $S = +1$ (kink) into the dislocation with $S = -1$ (antikink) and two dislocations the topological charges $S = +1$ has been found for the first time in the linear defect of a certain length. The decay of the topological defect is possibly due to the appearance of the local instability of the orientational twist mode of the director $\mathbf{n}$ in the defect core caused by the critical growth of hydrodynamic fluctuations with increasing applied voltage. It has been shown that the detected decay of the topological soliton is qualitatively well described by the perturbed sine-Gordon equation.