One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential | |
Zeng, Liangwei1,2; Zeng, Jianhua1,2 | |
刊名 | Nonlinear Dynamics |
2019-10-01 | |
卷号 | 98期号:2页码:985-995 |
关键词 | Fractional calculus Cubic–quintic nonlinearity Nonlinear Schrödinger equation Gap solitons |
ISSN号 | 0924090X;1573269X |
DOI | 10.1007/s11071-019-05240-x |
产权排序 | 1 |
英文摘要 | Competing nonlinearities, such as the cubic (Kerr) and quintic nonlinear terms whose strengths are of opposite signs (the coefficients in front of the nonlinearities), exist in various physical media (in particular, in optical and matter-wave media). A benign competition between self-focusing cubic and self-defocusing quintic nonlinear nonlinearities (known as cubic–quintic model) plays an important role in creating and stabilizing the self-trapping 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 equation (NLFSE), therefore obtaining the cubic–quintic or the purely quintic NLFSE, and investigate the propagation and stability properties of self-trapped modes therein. Two types of one-dimensional localized gap modes are found, including the fundamental and dipole-mode gap solitons. Employing the techniques based on the linear-stability analysis and direct numerical simulations, we get the stability regions of all the localized modes; and particularly, the anti-Vakhitov–Kolokolov criterion applies for the stable portions of soliton families generated in the frameworks of quintic-only nonlinearity and competing cubic–quintic nonlinear terms. © 2019, Springer Nature B.V. |
语种 | 英语 |
出版者 | Springer Netherlands |
内容类型 | 期刊论文 |
源URL | [http://ir.opt.ac.cn/handle/181661/31905] |
专题 | 西安光学精密机械研究所_瞬态光学技术国家重点实验室 |
作者单位 | 1.State Key Laboratory of Transient Optics and Photonics, Xi’an Institute of Optics and Precision Mechanics of Chinese Academy of Sciences, Xi’an; 710119, China; 2.University of Chinese Academy of Sciences, Beijing; 100049, China |
推荐引用方式 GB/T 7714 | Zeng, Liangwei,Zeng, Jianhua. One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential[J]. Nonlinear Dynamics,2019,98(2):985-995. |
APA | Zeng, Liangwei,&Zeng, Jianhua.(2019).One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential.Nonlinear Dynamics,98(2),985-995. |
MLA | Zeng, Liangwei,et al."One-dimensional gap solitons in quintic and cubic–quintic fractional nonlinear Schrödinger equations with a periodically modulated linear potential".Nonlinear Dynamics 98.2(2019):985-995. |
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