Solitary and traveling wave solutions to nematic liquid crystal equations using Jacobi elliptic functions

In our paper we apply the Jacobi elliptic function (JEF) expansion method to obtain exact solutions to the system of equations governing nematic liquid crystals, a system of high importance in nonlinear optics with numerous physical applications. We obtain solutions that are second-order polynomials in terms of JEFs for both the wave function and the tilt angle of molecular orientation. The solutions differ from previously obtained solutions in including both traveling and solitary wave solutions, with and without chirp. They also include the longitudinal dependence of coefficients in the equations, allowing for the management of both the dispersion and diffraction. Only two parameters of the differential equation need to be defined in terms of other coefficients, providing a wide range of flexibility when it comes to constructing solutions.