Results in Physics (Aug 2021)
On exploring optical solutions to the Hirota equation through an efficient analytical method
Abstract
In this paper, a direct approach, namely the generalized exponential rational function method is utilized to extract diverse collection of exact solutions to the (2+1)-dimensional Hirota equation. The equation is a widely used tools to describe the interactions of traveling waves in plasma physics. The new method provides more systematical and convenient handling of the process of nonlinear wave equations with the aid of computational software (Mathematica). Moreover, all of the obtained solutions are constructed with distinct structures, including sine–cos, tanh–coth, sinh–cosh and exponential in rational functions. Some of them are presented in contour plots to show the behavior of traveling wave solutions. It is clear to see that the proposed methodology is very simple, straightforward, and yet very powerful, and able to introduce very diverse categories of solutions in a single framework. The derived results confirm that the generalized exponential rational function method can solve other complex equations in nonlinear fields.
