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We introduce a system of fractional nonlinear Schroedinger equations (FNLSEs) which model the copropagation of optical waves carried by different wavelengths or mutually orthogonal circular polarizations in fiber-laser cavities with the…
The fractional Schr\"{o}dinger equation (FSE) -- a natural extension of the standard Schr\"{o}dinger equation -- is the basis of fractional quantum mechanics. It can be obtained by replacing the kinetic-energy operator with a fractional…
We investigate the spectral and dynamical properties of the fractional nonlinear Schr\"odinger (fNLS) equation with harmonic confinement. In this setting, the classical Laplacian is replaced by its fractional power…
Signal propagation in an optical fiber can be described by the nonlinear Schr\"odinger equation (NLSE). The NLSE has no known closed-form solution, mostly due to the interaction of dispersion and nonlinearities. In this paper, we present a…
We investigate the space time fractional nonlinear Schrodinger equation (FNLSE) incorporating the modified Riemann Liouville derivative introduced by Jumari. The equation is characterized by two parameters: the fractional derivative…
We develop a general analytical framework for determining the probability distribution of random nonlinear wave fields governed by the focusing nonlinear Schr\"odinger equation (fNLSE) in regimes where typical realizations are dominated by…
In this paper, we firstly extend the Fourier neural operator (FNO) to discovery the soliton mapping between two function spaces, where one is the fractional-order index space $\{\epsilon|\epsilon\in (0, 1)\}$ in the fractional integrable…
We conduct an experimental investigation of nonlinearity management in optics using femtosecond pulses and layered Kerr media consisting of glass and air. By examining the propagation properties over several diffraction lengths, we show…
Dynamics of solitons is considered in the framework of an extended nonlinear Schr\"odinger equation (NLSE), which is derived from a Zakharov-type model for wind-driven high-frequency (HF) surface waves in the ocean, coupled to damped…
In this research, numerical analysis of nonlinear pulse propagation is carried out. This is done mainly by solving the nonlinear Schrodinger equation using the split step algorithm. In a nonlinear media, dispersive effects exist…
The propagation of pulses in optical fibers is described by the generalized nonlinear Schrodinger equation (GNLSE), which takes into account the fiber losses, nonlinear effects, and higher-order chromatic dispersion. The GNLSE is a partial…
We present a full-wave Maxwell-density matrix simulation tool including c-number stochastic noise terms for the modeling of the spatiotemporal dynamics in active photonic devices, such as quantum cascade lasers (QCLs) and quantum dot (QD)…
The existence regimes and dynamics of soliton molecules in dispersion-managed (DM) optical fibers have been studied. Initially we develop a variational approximation (VA) for description of periodic dynamics of a soliton molecule within…
In this paper, we extend the Petviashvili method (PM) to the fractional nonlinear Schr\"{o}dinger equation (fNLSE) for the construction and analysis of its soliton solutions. We also investigate the temporal dynamics and stabilities of the…
The propagation of ultrashort pulses in optical fibre displays complex nonlinear dynamics that find important applications in fields such as high power pulse compression and broadband supercontinuum generation. Such nonlinear evolution…
We present an open-source multimode nonlinear Schr\"odinger equation-based simulation to investigate spatiotemporal nonlinear pulse propagation in thin-film silicon nitride (SiN) waveguides. Using this framework, we analyze femtosecond…
This review article provides a concise summary of one- and two-dimensional models for the propagation of linear and nonlinear waves in fractional media. The basic models, which originate from fractional quantum mechanics and more…
We elaborate a fractional discrete nonlinear Schr\"{o}dinger (FDNLS) equation based on an appropriately modified definition of the Riesz fractional derivative, which is characterized by its L\'{e}vy index (LI). This FDNLS equation…
The nonlinear pulse propagation in an optical fibers with varying parameters is investigated. The capture of moving in the frequency domain femtosecond colored soliton by a dispersive trap formed in an amplifying fiber makes it possible to…
We investigate the application of fractional calculus to model stellar dynamics, focusing on Resonant Relaxation (RR) near a supermassive black hole (SMBH). Standard theories use the local Fokker-Planck (FP) equation, restricted to Gaussian…