Construction of optical solitary wave solutions and their propagation for Kuralay system using tanh-coth and energy balance method

In this article, we study the complex coupled Kuralay system (CKS), which have many applications in different field such as ferromagnetic material and fiber optics. We implement an analytical method, namely, the tanh–coth method to considered system to formulate a system of algebraic equations. Solving the obtained system, we acquire different traveling wave solutions that are expressed in term of hyperbolic tangent functions and hyperbolic cotangent functions. Also, we employ the energy balance technique to the selected model to sort out the behavior of traveling wave solutions. By this method, we obtain periodic wave solution that are expressed in term of cosine function. In order to show the graphical presentation of the acquired solitary waves solutions, 3D and 2D curve are created by selecting well-suited parametric values via Mathematica.