相关论文: Exactly solvable model for nonlinear pulse propaga…

The nonlinear Schr\"odinger equation (NLSE) is a rich and versatile model, which in one spatial dimension has stationary solutions similar to those of the linear Schr\"odinger equation as well as more exotic solutions such as solitary waves…

We study the short pulse dynamics in the deterministic and stochastic environment in this thesis. The integrable short pulse equation is a modelling equation for ultra-short pulse propagation in the infrared range in the optical fibers. We…

A regularized $\alpha-$system of the Nonlinear Schr\"{o}dinger Equation (NLS) with $2\sigma$ nonlinear power in dimension $N$ is studied. We prove existence and uniqueness of local solution in the case $1 \le \sigma <\frac{4}{N-2}$ and…

We show the global well-posedness of the nonlinear Schr\"odinger equation with periodically varying coefficients and a small parameter $\varepsilon>0$, which is used in optical-fiber communications. We also prove that the solutions converge…

In the present paper we study the following scaled nonlinear Schr\"odinger equation (NLS) in one space dimension: \[ i\frac{d}{dt} \psi^{\varepsilon}(t) =-\Delta\psi^{\varepsilon}(t) +…

In this paper, we study the evolution of intensive light pulses in nonlinear single-mode fibers. The dynamics of light in such fibers is described by the nonlinear Schr\"odinger equation with the Raman term, due to stimulated Raman…

We analyze the spatiotemporal solitary waves of a graded-index multimode optical fiber with a parabolic transverse index profile. Using the nonpolynomial Schr\"odinger equation approach, we derive an effective one-dimensional Lagrangian…

We introduce a new notion of linear stability for standing waves of the nonlinear Schr\"odinger equation (NLS) which requires not only that the spectrum of the linearization be real, but also that the generalized kernel be not degenerate…

We report a generalized nonlinear Schr\"odinger equation simulation model of an extreme learning machine (ELM) based on optical fiber propagation. Using the MNIST handwritten digit dataset as a benchmark, we study how accuracy depends on…

The formation of extreme localizations in nonlinear dispersive media can be explained and described within the framework of nonlinear evolution equations, such as the nonlinear Schr\"odinger equation (NLS). Within the class of exact NLS…

In this paper we study the smoothness properties of solutions to a one-dimensional coupled nonlinear Schr\"{o}dinger system equations that describes some physical phenomena such as propagation of polarized laser beams in birefringent Kerr…

Extensive numerical simulations were performed to investigate all stages of modulation instability development from the initial pulse of pico-second duration in photonic crystal fiber: quasi-solitons and dispersive waves formation, their…

In this paper, we consider the derivative nonlinear Schr\"odinger (DNLS) equation. While the existence theory has been intensely studied, properties like dispersive estimates for the solutions have not yet been investigated. Here we address…

I present an overview of pulse propagation methods used in nonlinear optics, covering both full-field and envelope-and-carrier methods. Both wideband and narrowband cases are discussed. Three basic forms are considered -- those based on (a)…

A nonlinear Schr\"{o}dinger (NLS) equation with an effect of viscosity is derived from a Korteweg-de Vries (KdV) equation modified with viscosity using the method of multiple time-scales. It is well known that the plane-wave solution of the…

The defocusing nonlinear Schr\"odinger (NLS) equation is studied for a family of step-like initial data with piecewise constant amplitude and phase velocity with a single jump discontinuity at the origin. Riemann-Hilbert and steepest…

We study the Schr\"odinger equation which comes from the paraxial approximation of the Helmholtz equation in the case where the direction of propagation is tilted with respect to the boundary of the domain. In a first part, a mathematical…

In this paper, we present the two-dimensional generalized nonlinear Schr\"odinger equations with the Lax pair. These equations are related to many physical phenomena in the Bose-Einstein condensates, surface waves in deep water and…

The nonlinear propagation of ultrashort pulses in optical fiber depends sensitively on both input pulse and fiber parameters. As a result, optimizing propagation for specific applications generally requires time-consuming simulations based…

In this paper we consider a family of time-dependent 1-dimensional cubic Schr\"odinger equation (NLS) with periodic potential. Exploiting semiclassical scaling and multiscale analysis, we derive an effective nonlinear Dirac equation, which…