Abstract
The fractional perturbed Gerdjikov–Ivanov (pGI) equation plays a momentous role in nonlinear fiber optics, especially in the application of photonic crystal fibers. Constructing traveling wave solutions to this equation is a very challenging task in physics and mathematics. In the current article, our main purpose is to give the classifications of traveling wave solutions of the fractional pGI equation. These results can help physicists to further explain the complex fractional pGI equation.
Highlights
Where u u(t, x) represents unknown functions about time Dαt u and Dαxu are the conformable fractional derivative t and space x, respectively. u is the complex conjugation of u. [12,13,14]
In Reference [17], Zulfiqar and Ahmad explored the optical solution of the fractional perturbed Gerdjikov–Ivanov (pGI) equation by the Tanh method and Tanhcoth method, respectively. e main purpose of this paper is to give the classifications of traveling wave solutions of the fractional pGI equation by using the complete discrimination system method for polynomial, which is an important method to find the exact traveling wave solution of the fractional partial differential equation (FPDE)
The traveling wave solution of the fractional pGI equation is studied by using the complete discrimination system method
Summary
The traveling wave solution of the fractional pGI equation has attained a lot of interest in the filed of nonlinear science. Some explicit traveling wave solutions of the fractional pGI equation have been reported [15,16,17]. In Reference [15], Li and his collaborators studied the space-time fractional pGI equation by the fractional H-expansion method.
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