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We study local and global existence and smoothing properties for the initial value problem associated to a higher order nonlinear Schr\"odinger equation with constant coefficients which appears as a model for propagation of pulse in optical…

Analysis of PDEs · Mathematics 2013-10-30 Mauricio Sepulveda , Octavio Vera

Small quantum fluctuations in solitons described by the cubic-quintic nonlinear Schr\"{o}dinger equation (CQNLSE) are studied with the linear approximation. The cases of both self-defocusing and self-focusing quintic term are considered (in…

Quantum Physics · Physics 2007-05-23 Ray-Kuang Lee , Yinchieh Lai , Boris A. Malomed

Evolution by the Gross-Pitaevskii equation, which describes Bose-Einstein condensates under certain conditions, solves the unstructured search problem more efficiently than does the Schr\"odinger equation, because it includes a cubic…

Quantum Physics · Physics 2014-01-21 David A. Meyer , Thomas G. Wong

We study the spreading of initially localized states in a nonlinear disordered lattice described by the nonlinear Schr\"odinger equation with random on-site potentials - a nonlinear generalization of the Anderson model of localization. We…

Disordered Systems and Neural Networks · Physics 2010-05-11 M. Mulansky , A. Pikovsky

The dynamics of two pairs of counter-propagating waves in two-component media is considered within the framework of two generally nonintegrable coupled Sine-Gordon equations. We consider the dynamics of weakly nonlinear wave packets, and…

Pattern Formation and Solitons · Physics 2009-11-11 S. D. Griffiths , R. H. J. Grimshaw , K. R. Khusnutdinova

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…

Optics · Physics 2025-04-24 Yogesh Deo , Meenu Shrestha , Om Nath Acharya

We derive a non-linear sigma-model for the transport of light (classical waves) through a disordered medium. We compare this extension of the model with the well-established non-linear sigma-model for the transport of electrons…

Disordered Systems and Neural Networks · Physics 2009-10-31 B. Elattari , V. Kagalovsky , H. A. Weidenmueller

In this paper, we study a Schr\"odinger-type equation featuring a derivative in the nonlinear term and incorporating diffusion effects. This type of equation arises in various physical applications, such as modeling low-order magnetization…

Analysis of PDEs · Mathematics 2025-09-30 Juan Carlos Muñoz Grajales , Deissy Marcela Pizo

We show that the generalised nonlinear Schr\"{o}dinger equation (GNLSE) with quartic dispersion supports infinitely many multipulse solitons for a wide parameter range of the dispersion terms. These solitons exist through the balance…

Pattern Formation and Solitons · Physics 2021-06-30 Ravindra Bandara , Andrus Giraldo , Neil G. R. Broderick , Bernd Krauskopf

Motivated by recent experimental results, we demonstrate that the ubiquitous pulse propagation equation based on a single generalized nonlinear Schroedinger equation is incomplete and inadequate to explain the formation of the so called…

Optics · Physics 2013-05-31 Matteo Conforti , Andrea Marini , Daniele Faccio , Fabio Biancalana

A spectral mapping theorem is proved that resolves a key problem in applying invariant manifold theorems to nonlinear Schr\" odinger type equations. The theorem is applied to the operator that arises as the linearization of the equation…

solv-int · Physics 2007-05-23 F. Gesztesy , C. K. R. T. Jones , Y. Latushkin , M. Stanislavova

A two-dimensional generalized cubic nonlinear Schr\"odinger equation with complex coefficients for the group dispersion and nonlinear terms is used to investigate the evolution of a finite-amplitude localized initial perturbation. It is…

Plasma Physics · Physics 2015-05-27 Dian Zhao , M. Y. Yu

We model the effects of cross-phase modulation in frequency (or wavelength) division multiplexed optical communications systems, using a Schr\"odinger equation with a spatially and temporally random potential. Green's functions for the…

Optics · Physics 2009-11-07 A. G. Green , P. B. Littlewood , P. P. Mitra , L. G. L. Wegener

On the basis of a recently-proposed method to find solitary solutions of generalized nonlinear Schrodinger equations [1]-[3], the existence of an envelope solitonlike solutions of a nonlinear Schrodinger equation containing an anti-cubic…

Pattern Formation and Solitons · Physics 2009-11-07 R. Fedele , H. Schamel , V. I. Karpman , P. K. Shukla

We analytically study nonlinear quasi-monochromatic plasma waves in a two-dimensional electron system set between the two metal electrodes (gates). We derive a nonlinear Schrodinger equation for a slow-varying envelope to describe the…

Mesoscale and Nanoscale Physics · Physics 2025-08-29 A. A. Zabolotnykh

We consider the coupled propagation of an optical field and its second harmonic in a quadratic nonlinear medium governed by a coupled system of Schrodinger equations. We prove the existence of ring-profiled optical vortex solitons appearing…

Mathematical Physics · Physics 2025-06-23 Luciano Medina

We have investigated the nonlinear amplitude vector equation governing the evolution of optical pulses in optical and UV region. We are normalizing this equation for the cases of different and equal transverse and longitudinal size of…

Pattern Formation and Solitons · Physics 2015-06-26 L. M. Kovachev , L. M. Ivanov , D. Y. Dakova , L. I. Pavlov , K. L. Kovachev

We consider the nonlinear derivative Schrodinger equation with a quintic nonlinearity, on the one dimensional torus. We exhibit that the nonlinear dynamic properties consist of four frequency modes initially excited, whose frequencies…

Analysis of PDEs · Mathematics 2016-03-08 Hideo Takaoka

We study solitary wave solutions for the nonlinear Schr\"odinger equation perturbed by the effects of third-, and fourth-order dispersion, maintaining a wavenumber gap between the solitary waves and the propagation constant. We numerically…

Pattern Formation and Solitons · Physics 2024-04-17 O. Melchert , A. Demircan

We study the propagation of few-cycle optical solitary waves in a nonlinear media under the combined action of quadratic, cubic and quintic nonlinearities in a large phase-mismatched second harmonic (SHG) process. Exact bright and dark…

Optics · Physics 2014-01-16 Kanchan Kumar De , Amit Goyal , C. N. Kumar , Amarendra K. Sarma