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Influence of fractional time order on W-shaped and Modulation Instability gain in fractional Nonlinear Schrödinger Equation

Alphonse Houwe, Souleymanou Abbagari, Kottakkaran Sooppy Nisar, Mustafa Inc, Serge Y. Doka
2021 Results in Physics  
In this paper, we study the inuence of fractional time derivative on W-shaped prole and Modulation Instability gain in fractional Nonlinear Schrodinger Equation (NLSE) which could be used to describe the  ...  to the previous works reported in nonlinear optic bers [21, 50].  ...  Modulation Instability In this section, we analyze the behavior of the MI in the fractional time derivative in HOD to NLSE describing the propagation of the ultrashort pulses in nonlinear optical bers.  ... 
doi:10.1016/j.rinp.2021.104556 fatcat:6wko53dgwbddbpsjvi4oblxjqm

One-dimensional solitons in fractional Schrödinger equation with a spatially periodical modulated nonlinearity: nonlinear lattice

Liangwei Zeng, Jianhua Zeng
2019 Optics Letters  
The nonlinear potential landscape can balance the fractional-order diffraction and thus stabilizes the solitons, making the model unique and governed by the recently introduced fractional Schrödinger equation  ...  The existence and stability of stable bright solitons in one-dimensional (1D) media with a spatially periodical modulated Kerr nonlinearity are demonstrated by means of the linear-stability analysis and  ...  This work was supported, in part, by the Natural Science Foundation of China (project Nos. 61690224, 61690222), by the Youth Innovation Promotion Association of the Chinese Academy of Sciences (project  ... 
doi:10.1364/ol.44.002661 fatcat:gx33e5ctnvernkh3kntv3akvgi

Dynamics of Hermite–Gaussian beams in the linear and nonlocal nonlinear fractional Schrödinger equations

Zhenkun Wu, Yagang Zhang, Jingmin Ru, Yuzong Gu
2020 Results in Physics  
We analytically and numerically investigated the dynamics of the Hermite-Gaussian (HG) beams in linear and nonlocal nonlinear fractional Schrödinger equations (SEs), in both one and two dimensions.  ...  : Fractional schrödinger equations, Nonlocal nonlinearities, Hermite-Gaussian beams.  and characterize a local and strongly nonlocal medium, respectively. 0      Equation (1) can be numerically solved  ...  Introduction The fractional Schrödinger equation (fractional SE), first introduced in quantum mechanics by Lashkin [1] , has attracted considerable attention in the last decade [2] [3] [4] [5] [6] .  ... 
doi:10.1016/j.rinp.2020.103008 fatcat:bjdbbephwvhc5p5asdgjukqekm

On a fourth-order envelope equation for deep-water waves

Peter A. E. M. Janssen
1983 Journal of Fluid Mechanics  
The ordinary nonlinear Schrodinger equation for deep-water waves (found by a perturbation analysis to 0(€ 3 ) in the wave steepness €) compares unfavourably with the exact calculations of Longuet-Higgins  ...  Finally, we apply the Dysthe equations to a homogeneous random field of gravity waves and obtain the nonlinear energy-transfer function recently found by Dungey & Hui (1979).  ...  We remark that the nonlinear Schrodinger equation has only a restricted validity.  ... 
doi:10.1017/s0022112083000014 fatcat:47weffaldjentht7d5leu7jnsm

Heteroclinic Structure of Parametric Resonance in the Nonlinear Schrödinger Equation

M. Conforti, A. Mussot, A. Kudlinski, S. Rota Nodari, G. Dujardin, S. De Biévre, A. Armaroli, S. Trillo
2016 Physical Review Letters  
We show that the nonlinear stage of modulational instability induced by parametric driving in the defocusing nonlinear Schrödinger equation can be accurately described by combining mode truncation and  ...  averaging methods, valid in the strong driving regime.  ...  In this letter, taking the periodic defocusing nonlinear Schrödinger equation (NLSE) as a widespread example describing, e.g. periodic management of atom condensates [12, 19, 20, 22] , optical beam propagation  ... 
doi:10.1103/physrevlett.117.013901 pmid:27419569 fatcat:t7hendkmozc7tgx47tojkxniai

Nonlinear interactions between upper-hybrid and Alfvén modes in a magnetized plasma containing charged dust impurities

2006 Journal of Plasma Physics  
The coupled mode equations are then Fourier analyzed to obtain a new dispersion relation, which admits new classes of modulational instabilities.  ...  We consider the nonlinear interactions between upper-hybrid (UH) and Alfvén modes in a magnetized electron-ion plasma containing a fraction of stationary charged dust grains.  ...  Equation (10) is a nonlinear Schrödinger equation containing both cubic and non-local nonlinearities.  ... 
doi:10.1017/s0022377806004740 fatcat:52qxkspzpvgqpdub4d72p6w3c4

The fractional discrete nonlinear Schrödinger equation

Mario I. Molina
2019 Physics Letters A  
We study a fractional version of the two-dimensional discrete nonlinear Schrödinger (DNLS) equation, where the usual discrete Laplacian is replaced by its fractional form that depends on a fractional exponent  ...  We also compute the nonlinear modes and their stability for both, bulk and surface modes. The modulational stability is seen to increase with an increase in the fractional exponent.  ...  Figure 6 . 6 (a) Modulational instability gain versus nonlinearity strength.  ... 
doi:10.1016/j.physleta.2019.126180 fatcat:6ie6266ez5bwhfklfqo445w52m

On the stability of weakly nonlinear short waves on finite-amplitude long gravity waves

Jun Zhang, W. K. Melville
1992 Journal of Fluid Mechanics  
The modulated nonlinear Schrodinger equation (Zhang & Melville 1990), describing the evolution of a weakly nonlinear short-gravity-wave train riding on a longer finite-amplitude gravity-wave train is used  ...  Approximate analytical solutions and numerical solutions show that the conventional sideband (Benjamin-Feir) instability is just the first in a series of resonantly unstable regions which increase in number  ...  Thus the ratio of the nonlinearity to dispersion terms in the modulated Schrodinger equation changes along the long wave.  ... 
doi:10.1017/s0022112092002635 fatcat:zeha5hvzu5c43nf6nefhabylze

Airy-Gaussian vortex beams in the fractional nonlinear-Schrödinger medium [article]

Shangling He, Kangzhu Zhou, Boris A. Malomed, Dumitru Mihalache, Liping Zhang, Jialong Tu, You Wu, Jiajia Zhao, Xi Peng, Yingji He, Xiang Zhou, Dongmei Deng
2021 arXiv   pre-print
We address the propagation of vortex beams with the circular Airy-Gaussian shape in a (2+1)-dimensional optical waveguide modeled by the fractional nonlinear Schrodinger equation.  ...  Under the action of the azimuthal modulational instability, an axisymmetric beam may split into a set of separating bright spots.  ...  the action of the azimuthal modulational instability.  ... 
arXiv:2110.00185v1 fatcat:wcc3kb2chfdudjfjjxjuhueku4

Symmetry breaking of spatial Kerr solitons in fractional dimension [article]

Pengfei Li, Boris A. Malomed, Dumitru Mihalache
2020 arXiv   pre-print
We study symmetry breaking of solitons in the framework of a nonlinear fractional Schrödinger equation (NLFSE), characterized by its Lévy index, with cubic nonlinearity and a symmetric double-well potential  ...  Second, a family of asymmetric solutions branches off from antisymmetric states in the case of self-defocusing nonlinearity through a bifurcation of an inverted-pitchfork type.  ...  The nonlinear fractional Schrödinger equation We start the analysis by considering beam propagation along the z-axis in a waveguide with the Kerr nonlinearity.  ... 
arXiv:2003.14161v1 fatcat:s5cmrtok6vhgzpo7apyfm4sibe

Vortex solitons in fractional nonlinear Schrödinger equation with the cubic-quintic nonlinearity [article]

Pengfei Li, Boris A. Malomed, Dumitru Mihalache
2020 arXiv   pre-print
We address the existence and stability of vortex-soliton (VS) solutions of the fractional nonlinear Schrödinger equation (NLSE) with competing cubic-quintic nonlinearities and the Lévy index (fractionality  ...  Unlike the usual two-dimensional NLSE (which corresponds to α = 2), in the fractional model VSs exist above a finite threshold value of the total power,P.  ...  In particular, the 1D Schrödinger equation with the cubic term subject to singular spatial modulation may emulate fractional dimension 0 < D < 1 [81] .  ... 
arXiv:2003.14137v1 fatcat:5mpjf7hp3jcojl4oo35qsrokyi

Self-Phase Modulation in Optical Fiber Communications: Good or Bad?

Govind P. Agrawal
2007 2007 Conference on Lasers and Electro-Optics (CLEO)  
chirped. • As a pulse propagates along the fiber, its spectrum changes because of SPM. 5/100 Back Close Nonlinear Phase Shift • Pulse propagation governed by Nonlinear Schrödinger Equation i ∂ A ∂  ...  Nonlinear Schrödinger Equation i ∂ A ∂ z − β 2 2 ∂ 2 A ∂t 2 + γ|A| 2 A = 0. • CW solution unstable for anomalous dispersion (β 2 < 0). • Useful for producing ultrashort pulse trains at tunable repetition  ...  are also useful for enhancing the nonlinear effects. • SPM and XPM effects in such highly nonlinear fibers are likely to find new applications.  ... 
doi:10.1109/cleo.2007.4453562 fatcat:zrmmxyfdfnd5xbm2qfbpym5svq

One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential

Liangwei Zeng, Jianhua Zeng
2019 Nonlinear dynamics  
of D-dimensional localized structures, in the contexts of standard nonlinear Schrödinger equation.  ...  We incorporate an external periodic potential (linear lattice) into this model and extend it to the space-fractional scenario that begins to surface in very recent years—the nonlinear fractional Schrödinger  ...  ACKNOWLEDGMENTS This work was supported, in part, by the the Natural Science Foundation of China (project Nos. 61690222, 61690224), and by the Youth Innovation Promotion Association of the Chinese Academy  ... 
doi:10.1007/s11071-019-05240-x fatcat:wv22iwrigzfchf7pny3yq2jdlq

Semiclassical relativistic fluid theory for electrostatic envelope modes in dense electron–positron–ion plasmas: Modulational instability and rogue waves

2013 Journal of Plasma Physics  
A multiscale perturbative method is used to derive a nonlinear Schrödinger equation for the envelope amplitude.  ...  Criteria for modulational instability, which occurs for small values of the carrier wavenumber (long carrier wavelengths), are derived. The occurrence of rogue waves is briefly discussed.  ...  Michael Mc Kerr acknowledges support from the Department of Employment and Learning -Northern Ireland (DEL NI) in the form of a PhD studentship.  ... 
doi:10.1017/s0022377813001323 fatcat:sq7j6xlrnrghvpv5y23znhzscy

Modulation Instability, Four-Wave Mixing and their Applications [chapter]

Tobias Hansson, Alessandro Tonello, Stefano Trillo, Stefan Wabnitz
2017 Shaping Light in Nonlinear Optical Fibers  
. Introduction Modulation instability (MI) of a continuous wave (CW) background solution of the nonlinear Schrödinger (NLS) equation is a well-known phenomenon that occurs in a variety of fields, such  ...  This process can be described in terms of exact solutions of the NLS equation [9][10][11][12], and has been experimentally observed in different physical settings, such as deep water waves [13, 14], in  ...  .  Akhmediev, N. and Korneev, V. (1986) Modulation instability and periodic solutions of the nonlinear Schrödinger equation.  ... 
doi:10.1002/9781119088134.ch1 fatcat:ucbxc4h3yfec7m5jng2jpm2qsu
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