Exact solutions of paraxial equation via extended hyperbolic function method.

In this article, we analyze the traveling wave solutions of the dimensionless time dependent Paraxial equation. In Paraxial approximation the partial differential approximation is responsible for optical wave propagation. The proposed equation is used when light or electric currents pass through optical systems such as lenses, mirrors, and optical fibers. An extended hyperbolic function method is used to construct traveling wave solutions. By using the proposed method in the Paraxial equation, different types of soliton solutions such as dark solitons, bright solitons, periodic solutions and singular soliton solutions are recovered. These solutions are obtained by carefully choosing the values of certain parameters involved in the method and model. Our findings are original and can greatly contribute to understanding the propagation of light waves. Some important requirements for the validity of solutions are also discussed. In addition, line plots and surface diagrams are presented to demonstrate the physical and behavioral significance of our findings for the proposed model. [ABSTRACT FROM AUTHOR]