Shape changing nonlocal molecular deformations in a nematic liquid crystal system

Abstract

The nature of nonlinear molecular deformations in a homeotropically aligned nematic liquid crystal (NLC) is presented. We start from the basic dynamical equation for the director axis of a NLC with elastic deformation and mapped onto a integro-differential perturbed Nonlinear Schro¨dinger equation which includes the nonlocal term. By invoking the modified extended tangent hyperbolic function method aided with symbolic computation, we obtain a series of solitary wave solutions. Under the influence of the nonlocality induced by the reorientation nonlinearity due to fluctuations in the molecular orientation, the solitary wave exhibits shape changing property for different choices of parameters. This intriguing property as a result of the relation between the coherence of the solitary deformation and the nonlocality reveals a strong need for a deeper understanding in the theory of self-localization in NLC systems.

Assorted Spatial Optical Dynamics of a Generalized Fractional Quadruple Nematic Liquid Crystal System in Non-Local Media

“…The MSEM provides the possibility of merging two linear differential equations with different orders. In our case, Equation (22) and Equation (28) provide…”

“…Case 1. The unknown function ϕ can be determined directly by solving the linear ordinary differential equations that appear in Equation (22), Equation (23), Equation (27), or Equation (28). With the first choice, we obtain…”

“…Many researchers have studied Equations ( 1) and ( 2), with the abovementioned types of nonlinearity. Some of these attempts were as follows: the extended sinh-Gordon equation expansion method [22], the exp(−ϕ(ξ))-expansion method [23], the extended trial equation method [24], the extended simplest equation technique, the modified Khater and modified Kudryashov methods [25], the tan(ϕ/2)-expansion method [26], the generalized exponential rational function method [27], and the modified extended tangent hyperbolic function method [28]. The conservation laws of the liquid crystal model were derived in [29,30].…”

Novel constructed dark, bright, and rogue waves of three models of the well-known nonlinear Schrödinger equation

“…In this article, we study the bright and dark soliton solutions of the above-mentioned models that are given, respectively [25,26,27,28,29,30,31,32,33]…”

“…The following is the sequence in which the sections of the remainder of the paper show up: In section 2, some unique soliton wave solutions of the above-mentioned models are constructed using the suggested analytical technique [25,26,34]. In addition, the numerical analysis of the obtained solutions shows new characterizations of the studied models.…”