Ismail Onder

Yildiz Technical University · Department of Mathematical Engineering

Purpose: In this paper, optical solitons of higher-order nonlinear Schrödinger equation with Kudryashov's sextic power-law of nonlinear refractive index are investigated via the direct mapping method. The considered model identifies the optical soliton pulse propagation in the optical fibers. Deriving the optical solutions of investigated model suc...

We have discussed the perturbed Gerdjikov-Ivanov (pGI) equation describing optical pulse propagation (PP) with perturbation effects, which has various applications in optical fibers, especially in photonic crystal fibers. According to our literature review, we have discovered new and original soliton types using the Sardar sub-equation and the modi...

We have discussed the perturbed Gerdjikov-Ivanov (pGI) equation describing optical pulse propagation (PP) with perturbation effects, which has various applications in optical fibers, especially in photonic crystal fibers. According to our literature review, we have discovered new and original soliton types using the Sardar sub-equation and the modi...

Purpose In this study, we investigated the time-fractional coupled nonlinear Schrödinger (TF-CNLS) system in conformable fractional sense. TF-CNLS system models the circularly-polarized waves in the optic branch of physics frequently. Methodology To obtain optical solitons of the model via new Kudryashov method and Kudryashov auxiliary equation me...

Purpose: When it comes to third and higher-order dispersion, the Schrödinger–Hirota equation is one of the main models developed outside the classical NLSE management models for optical soliton transmission. The cubic–quartic Fokas–Lenells equation is also one of the recently developed equations, which has importance in the field of telecommunicati...

In this work, we aim to derive various soliton solutions to the Wazwaz–Benjamin–Bona–Mahony equation with conformable and M-truncated derivatives. The considered equation models long waves in the ocean engineering field. Unified Riccati equation expansion and Kudryashov auxiliary equation methods are used to the model, and so, kink, singular, and p...

In this study, we have focused on finding soliton solutions of the cubic–quartic Fokas–Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. The main motivation of this study is to produce new solutions with previously unused methods for data transmission models in fiber optic cabl...

In this study, we have focused on finding soliton solutions of the cubic-quartic Fokas-Lenells equation, which models the nonlinear pulse transmission through optical fiber, is a pretty new and updated model. We have used three different efficient analytical methods, namely, the Sinh-Gordon expansion method, enhanced modified extended tanh expansio...

This paper extracts some analytical solutions of simplified modified Camassa-Holm (SMCH) equations with various derivative operators, namely conformable and M-truncated derivatives that have been recently introduced. The SMCH equation is used to model the unidirectional propagation of shallow-water waves. The extended rational sine−cosine and sinh−...

We introduce optical soliton solutions of the Kundu–Mukherjee–Naskar (KMN) equation by using the Sardar subequation (SSM) and the new Kudryashov methods (nKM). The KMN equation plays an important role in modeling the fiber pulse in optics, the rogue waves in the oceans and the bending of the light beam. In order to motivate and contribute to resear...

In this paper, the time-fractional Jaulent–Miodek system associated with energy-dependent Schrödinger potential is solved by the modified Laplace decomposition method. The Caputo fractional derivative is considered throughout the paper. The attained solutions using the method are analyzed and compared with the solutions of the existing studies in t...

This paper considers deriving new exact solutions of a nonlinear complex generalized Zakharov dynamical system for two different definitions of derivative operators called conformable and $ M- $ truncated. The system models the spread of the Langmuir waves in ionized plasma. The extended rational $ sine-cosine $ and $ sinh-cosh $ methods are used t...

In this study, we investigate the nonlinear Zoomeron equation by using the extended rational sin - cos and sinh - cosh methods. We successfully constructed some important solutions such as singular periodic wave, periodic wave, topological, and singular soliton solutions. Using suitable parameter values, we present the numerical simulations to some...

In this research, our main motivation is to find the novel analytical solutions of \((2+1)\) dimensional Heisenberg ferromagnetic spin equation, which describes the nonlinear dynamics of the ferromagnetic materials by using the extended rational \(sine-cosine\) and \(sinh-cosh\) methods. The considered PDE is converted to an ODE by applying a wave...

In this paper, we study the novel exact solutions of the (2+1)−dimensional Biswas-Milovic equation for the description of pulse propagation in optical fiber. We successfully constructed some important solutions, such as dark, singular, combined dark-singular soliton, singular periodic wave and rational function solutions, have been analytically obt...

In this paper, the system of singularly Perturbed Reaction-Diffusion p roblems w hich a re commonly used in physics and chemistry branches of science, were investigated. Sinc-Galerkin Method was used to obtaining the solution of problems. Because of there is no article about Sinc-Galerkin Method related to singularly perturbed Reaction-Diffusion pr...