Exact and approximate solutions for optical solitary waves in nematic liquid crystals

The equations governing optical solitary waves in nonlinear nematic liquid crystals are investigated in both (1+1) and (2+1) dimensions. An isolated exact solitary wave solution is found in (1+1) dimensions and an isolated, exact, radially symmetric solitary wave solution is found in (2 + 1) dimensions. These exact solutions are used to elucidate what is meant by a nematic liquid crystal to have a nonlocal response and the full role of this nonlocal response in the stability of (2 + 1) dimensional solitary waves. General, approximate solitary wave solutions in (1+1) and (2+1) dimensions are found using variational methods and they are found to be in excellent agreement with the full numerical solutions. These variational solutions predict that a minimum optical power is required for a solitary wave to exist in (2 + 1) dimensions, as confirmed by a careful examination of the numerical scheme and its solutions. Finally, nematic liquid crystals subjected to two different external electric fields can support the same solitary wave, exhibiting a new type of bistability. (C) 2014 Elsevier B.V. All rights reserved.