W-shaped surfaces to the nematic liquid crystals with three nonlinearity laws

TLDR: The investigation of nematic liquid crystals, using the proposed method, shows that there is diversity between the solutions gained via this method with those obtained via different methods, and the constraint conditions to guarantee the existence of the solutions are used.

Abstract: In this work, we attempt to construct some novel solutions of nematicons within liquid crystals including three types of nonlinearity namely Kerr, parabolic, and power law, using the generalized exponential rational function method. The investigation of nematic liquid crystals, using the proposed method, shows that there is diversity between the solutions gained via this method with those obtained via different methods. Further, we use the constraint conditions to guarantee the existence of the solutions. The W-shaped surfaces, dark soliton, bright soliton, singular soliton, period singular soliton, periodic waves, and complex solutions of the studied equations are successfully constructed. Moreover, some obtained solutions are drawn to a better understanding of the characteristics of nematicons in liquid crystals.