Destruction of shape-invariant solitons in nematic liquid crystals by noise
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We investigate the destructive influence of noise on the shape-invariant solitons in a three-dimensional model that includes the highly nonlocal nature of nematic liquid crystals. We first determine the fundamental shape-preserving solitons and then establish that any noise added to the medium or to the solitons induces them to breathe at short propagation distances and to disperse at long propagation distances. The characteristics of breathing solitons at short distances are well predicted by the variational calculation. At longer propagation distances soliton beams suddenly spread, almost without radiation losses. Their power remains almost conserved until they reach the transverse boundaries of the sample. The increase in the amount of noise accelerates beam spreading and soliton destruction. The influence of the correlation length of noise is more complex. An initial increase in the correlation length causes solitons to disperse at shorter propagation distances. However, further increase in the correlation length leads to a reversal - to prolonged stability and dispersal at longer propagation distances. We give theoretical explanation for such behavior in terms of mean-field evolution equations. 2013 American Physical Society.