Classification of All Single Traveling Wave Solutions of Fractional Perturbed Gerdjikov–Ivanov Equation

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.

On the optical soliton solutions to the fractional complex structured (1+1)-dimensional perturbed gerdjikov-ivanov equation

“…Besides these, there are some actual articles given fractional calculus about FPGIE, such as M-fractional PGIE [33], Riemann-Liouville FPGI model [34], and FPGIE in conformable sense [35]. In addition, conservation laws for PGIE with Lie symmetries [36], abundant wave solutions [37], novel optical solitons [38], fractional form [39]. Computational extracting solutions [40].…”

Investigation of optical soliton solutions for the perturbed Gerdjikov-Ivanov equation with full-nonlinearity

“…Besides all, there are some actual papers in view of fractional calculus about pGI equation such as M-fractional pGI equation [51] , fractional pGI in conformable sense [52] and Riemann-Liouville fractional pGI model [53] . In addition, conservation laws for pGI with Lie symmetries [54] , abundant wave solutions [55] , new solitary wave solutions [56] , fractional form [57] , novel optical solitons [58] and computational extracting solutions [59] .…”

Phase Portraits and Traveling Wave Solutions of Fokas System in Monomode Optical Fibers

“…In recent years, the complex nonlinear partial differential equations [1][2][3][4] have been widely used in nonlinear optics, fluid mechanics, quantum mechanics, biology, communication, control, and other fields [5][6][7][8][9], which mainly include the wellknown Schrödinger equation [10], the Radhakrishnan-Kundu-Lakshmanan equation [11], the Kundu-Mukherjee-Naskar equation [12], the Lakshmanan-Porsezian-Daniel equation [13], the Triki-Biswas equation [14], the Fokas-Lenells equation [15], the Gerdjikov-Ivanov equation [16], the Ginzburg-Landau equation [17], and the Biswas-Arshed equation [18]. The study of dynamic behavior and exact traveling wave solutions of complex nonlinear partial differential equations has always been a very important hot topic.…”