In this study, lump, lump one-strip, lump two-strip, rogue wave, manifold periodic type exact solutions are produced via appropriate transformation scheme by taking into account the Kerr Law properties of the model defining nematic liquid crystals. The various transformations are considered in the form containing positive quadratic functions, trigonometric, exponential and hyperbolic functions respectively. In addition we have generated Ma-breather (MB), Kuznetsov-Ma breather (KMB) and its relating rogue wave solutions for proposed model. The resulting solutions of the model play an significant character in the energy transport in soliton molecules in liquid crystals. Furthermore, the wave behaviours for diverse values of constants in the attained exact solutions are explained. 

Discussion on rational solutions for Nematicons in liquid crystals with Kerr Law

Stability analysis and solutions of (2 + 1)-Kadomtsev–Petviashvili equation by homoclinic technique based on Hirota bilinear form

Analytical solutions and physical interpretations for the shallow water wave system, which is the modeling of a physical phenomenon in applied mathematics, are presented in this study. The solutions of the shallow water wave system, which models the formation, interaction and breaking of shallow water waves on the ocean surface as a result of external effects (e.g., wind), are examined using the modified expansion method. Besides, physically, the differences between deep and shallow water waves and their transitions with each other are examined. Hyperbolic and trigonometric wave solutions are produced with the advantages of the modified expansion method over other traditional methods. In these wave solutions, the values that cause the breaking of the wave are calculated by considering the velocity parameter. The behavior of the wave at these values is presented with the help of simulations. Finally, the states of solitary wave solutions concerning each other in the same system are compared and analyzed according to the velocity parameter.

Breaking analysis of solitary waves for the shallow water wave system in fluid dynamics

Investigation of internal dynamics of soliton with the help of traveling wave soliton solution of Hamilton amplitude equation

Dynamics of traveling wave solutions arising in fiber optic communication of some nonlinear models

In this study, trigonometric and hyperbolic type traveling wave solutions are produced by using the sub-equation analytical method by taking into account the Kerr Law properties of the equation defining nematic liquid crystals. The resulting traveling wave solutions of the equation play an important role in the energy transport in soliton molecules in liquid crystals. In addition, the solitary wave behaviors obtained for different values of the constants in the produced traveling wave solutions are discussed. The hyperbolic type traveling wave solutions of the equation defining the nematic liquid crystals incorporating Kerr Law property is represented as dark and singular solitons. Ready-made package programs are used for algebraic operations and graphic drawings. It is emphasized that the analytical method is effective, useful and valid.

Bayhan Karabulut

Papers

Nematicons in liquid crystals with Kerr Law by sub-equation method