Abstract
In this research paper, we try to illustrate the structure of the novel exact soliton wave solutions of nematicons in liquid crystals with four law nonlinearity forms including the Kerr, power, parabolic and dual-power by utilizing the $$\tan (\phi /2)$$-expansion method. The aim of this research is not just to find the dark, bright, combined dark-bright, singular types, traveling and solitary solutions of nematicons in liquid crystals by investigating the aforementioned method, showing the differences between the obtained solutions and other solutions obtained by using different methods. Moreover, constraints guarantee the existence of the obtained solutions. Eventually, we believe that the enforced method is more powerful and efficient than other methods and the obtained solutions in this paper can help us to understand soliton molecules in liquid crystals. That will be extensively used to describe many interesting physical phenomena in the areas of gas, plasma, optics, acoustics, fluid dynamics, classical mechanics and so on.
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