Computational and approximate solutions of complex nonlinear Fokas–Lenells equation arising in optical fiber

Soliton: A dispersion-less solution with existence and its types

“…In the study of optical solitons, the nonlinear Schrodinger equation is crucial [ 48 ]. The Fokas-Lenells (FL) equation [ 49 , 50 ] has been derived as an alternate model equation of the Schrodinger equation for the higher-order terms, and it represents the propagation of short pulses in optical fibers. Complex perturbed Gerdjikov–Ivanov equation [ 51 ] describes the physical characterization of the optical soliton waves to mitigate internet bottlenecks with many different applications in the telecommunication industry.…”

“…In addition to the above equations, there are many equations which have important applications in field of science and technology and yields soliton type solutions i.e. Kolmogorov–Petrovskii–Piskunov equation [ 73 ], generalized (2 + 1)-dimensional shallow water waves equation [ 74 ], human immunodeficiency virus (HIV)-1 infection of CD4+ T-cells fractional biomathematical model for constructing novel solitary wave solutions [ 75 ], Fokas–Lenells equation [ 49 ], Klein–Fock–Gordon equation [ 76 ] relates to Schrodinger equation, phi-four equation [ 77 ] which is a particular case of the Klein–Fock–Gordon equation, telegraph equation [ 52 ], Chaffee–Infante equation [ 22 ], Benjamin–Bona–Mahony (BBM) [ 38 ], Cahn–Allen equation [ 78 ], Klein–Gordon–Zakharov equation [ 36 , 79 ], Kaup–Kupershmidt equation [ 23 ], Fisher-Kolmogorov-Petrovskii-Piskunov [ 80 ], Kadomtsev−Petviashvili equation [ 81 ], Ginzburg–Landau equation [ 82 ], Hirota–Satsuma–Shallow Water Wave Equation [ 83 ] (2 + 1)-dimensional Kadomtsev–Petviashvili–Benjamin–Bona–Mahony equation [ 84 ], cubic–quintic nonlinear Helmholtz model [ 85 ], Ostrovsky equation [ 13 ], Vakhnenko–Parkes equation which is reduced from the Ostrovsky equation [ 86 ], complex perturbed Gerdjikov–Ivanov (CPGI) equation [ 51 ], etc.…”

A new version of trial equation method for a complex nonlinear system arising in optical fibres

“…The complex nonlinear partial differential equations (CNPDEs) are considerably employed to represent a wide family of nonlinear systems in applied sciences. In particular the electromagnetic wave propagation, the light pulse propagation and the propagation of short pulses in optical fibres are modelled via several CNPDEs such as Kundu-Eckhaus equation (Bekir and Zahran 2020), complex Ginzburg-Landau equation (Isah and Yokus 2023), Schrödinger equation (Liu and Feng 2023), complex Fokas-Lenells equation (Khater et al 2021), Hirota Maccari system (Yokus and Baskonus 2022), complex Radhakrishnan-Kundu-Lakshmanan equation (Kudryashov 2022), Kundu-Mukherjee-Naskar equation (Wang et…”

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.…”