Wave behaviors of Kundu–Mukherjee–Naskar model arising in optical fiber communication systems with complex structure

Abstract

Rogue waves are very mysterious and extra ordinary waves. They appear suddenly even in a calm sea and are hard to be predicted. Although nonlinear Schrödinger equation (NLS) provides a perspective, it alone can neither detect rogue waves nor provide a complete solution to problems. Therefore, some approximations are still mandatory for both obtaining an exact solution and predicting rogue waves. Such as Kundu-Mukherjee-Naskar (KMN) model which allows obtaining lump-soliton solutions considered as rogue waves. In this study the functional variable method is utilized to obtain the analytical solutions of KMN model that corresponds to the propagation of soliton dynamics in optical fiber communication system.

Solving Conformable Fractional Differential Equations with ``EJS Software and Visualization of Sub-diffusion Process

“…In recent years, fractional differential equations (FDEs) in the sense of Riemann-Liouville, Caputo, and Grunwald-Letnikov have played an essential role in modeling various real-world issues. FDEs have been used to describe real-world events in many fields, such as diffusion and dynamics in biology, fluid mechanics, fluid flow, signal processing, and others [15,20,22,25,30,33]. An alternate formulation of the diffusion equation is presented to enhance anomalous diffusion modeling by employing a new derivative with fractional order known as the conformable derivative.…”

Optical soliton solutions of the conformable time fractional Radhakrishnan–Kundu–Lakshmanan Model

“…Different physical factors such as dispersion, material dispersion, diffraction and nonlinear response affect the pulse dynamics [3]. Soliton propagation has been represented mathematically by a variety of models such as Fokas-Lenells equation [4], Sasa-Satsuma equation [5], Chen-Lee-Liu equation [6], nonlinear Schrödinger's equation [7], Kundu-Mukherjee-Naskar equation [8], Kundu-Eckhaus equation [9], Schrödinger-Hirota equation [10] and Ginzburg-Landau model [11] Obtaining the exact solutions of the NLPDEs helps in understanding the relationship between a differential equation and its mathematical and physical applications. The exact traveling-wave solutions of NLPDEs have been constructed via various effective approaches which include exponential rational function method [12], extended trial function method [13], improved Bernoulli sub equation function method [14,15], Riccati-Bernoulli sub-ODE method [16].…”

New Optical Solitons in Bragg Grating Fibers for the Nonlinear Coupled ( 2 + 1 )-Dimensional Kundu-Mukherjee-Naskar System via Complete Discrimination System Method

“…In [4], Ekici et al indicated that the KMN equation is applicable to study the dynamics of soliton propagation through optical fibers in (2 + 1) dimensions on the bases of the fact that RWs are observed in a crystal fiber [5]. Note that the use of special methods constructing exact solutions of nonlinear differential models (see [6][7][8][9][10][11][12][13]) is a main research area of nonlinear optical science, the optical solitons in KMN equation have been addressed by broad researchers to recover the exact solutions by applying many effective methods including Kudryashov's approach method [14,15], the tanh function method [16], the new auxiliary equation method [17], the new extended direct algebraic method [18,19], the method of undetermined coefficients and Lie symmetry [20,21], the trial equation technique [22], the functional variable method [23], and the modified simple equation approach technique [24]. It is worth mentioning that Yldrm [25] also used the modified simple equation approach technique to discuss a new model of coupled KMN equations in birefringent fibers.…”