Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media

doi:10.1103/PhysRevE.99.052206

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	Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media
	Wang, Li 2,3; Malomed, Boris A.1,4; Yan, Zhenya2,3
刊名	PHYSICAL REVIEW E
	2019-05-09
卷号	99 期号:5 页码:10
ISSN号	2470-0045
DOI	10.1103/PhysRevE.99.052206
英文摘要	We introduce a model based on the one-dimensional nonlinear Schrodinger equation with critical (quintic) or supercritical self-focusing nonlinearity. We demonstrate that a family of solitons, which are unstable in this setting against the critical or supercritical collapse, is stabilized by pinning to an attractive defect, that may also include a parity-time (PT)-symmetric gain-loss component. The model can be realized as a planar waveguide in nonlinear optics, and in a super-Tonks-Girardeau bosonic gas. For the attractive defect with the delta-functional profile, a full family of the pinned solitons is found in an exact analytical form. In the absence of the gain-loss term, the solitons' stability is investigated in an analytical form too, by means of the Vakhitov-Kolokolov criterion; in the presence of the PT-balanced gain and loss, the stability is explored by means of numerical methods. In particular, the entire family of pinned solitons is stable in the quintic (critical) medium if the gain-loss term is absent. A stability region for the pinned solitons persists in the model with an arbitrarily high power of the self-focusing nonlinearity. A weak gain-loss component gives rise to intricate alternations of stability and instability in the system's parameter plane. Those solitons which are unstable under the action of the supercritical self-attraction are destroyed by the collapse. On the other hand, if the self-attraction-driven instability is weak and the gain-loss term is present, unstable solitons spontaneously transform into localized breathers, while the collapse does not occur. The same outcome may be caused by a combination of the critical nonlinearity with the gain and loss. Instability of the solitons is also possible when the PT-symmetric gain-loss term is added to the subcritical nonlinearity. The system with self-repulsive nonlinearity is briefly considered too, producing completely stable families of pinned localized states.
资助项目	NSFC (China)[11571346] ; NSFC (China)[11731014] ; NSFC (China)[61621003] ; Interdisciplinary Innovation Team of Chinese Academy of Sciences ; Chinese Academy of Sciences President's International Initiative (PIFI)
WOS研究方向	Physics
语种	英语
出版者	AMER PHYSICAL SOC
WOS记录号	WOS:000467400900002
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/34647]
专题	系统科学研究所
通讯作者	Yan, Zhenya
作者单位	1.Tel Aviv Univ, Ctr Light Matter Interact, IL-59978 Tel Aviv, Israel 2.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mechanizat, Beijing 100190, Peoples R China 3.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China 4.Tel Aviv Univ, Fac Engn, Sch Elect Engn, Dept Phys Elect, IL-59978 Tel Aviv, Israel
推荐引用方式 GB/T 7714	Wang, Li,Malomed, Boris A.,Yan, Zhenya. Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media[J]. PHYSICAL REVIEW E,2019,99(5):10.
APA	Wang, Li,Malomed, Boris A.,&Yan, Zhenya.(2019).Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media.PHYSICAL REVIEW E,99(5),10.
MLA	Wang, Li,et al."Attraction centers and parity-time-symmetric delta-functional dipoles in critical and supercritical self-focusing media".PHYSICAL REVIEW E 99.5(2019):10.