Abstract
The aim of this work is to explore and find new closed-form nematicon solutions for different nonlinearities which occur in nematic liquid crystals (NLC) along with proposing optical system application that utilizes NLC nonlinearities. In particular, Lie point symmetry method is employed to scrupulously inspect and acquire solutions for some interesting cases of nonlinearities which have not been fully examined in literature such as quadratic, generalized dual-power law, and eighth-order nonlinearities. A variety of different nematicon dynamics are observed, including bright solitons, dark solitons and periodic behaviors. The explicit solution form for each dynamical behavior is obtained and the solution dependence on model parameters is investigated. The proposed optical system enables the flexible realization of different types of NLC nonlinearities. To the best of our knowledge, this is the first time to attain explicit exact nontrivial solutions for the particular cases of generalized dual-power law and eighth-order nonlinearities.