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Existence of optical vortices in R-2
Guo, Qing1; Cao, Daomin2,3; Li, Hang2,3
AbstractOptical vortices are phase singularities nested in electromagnetic waves which constitute a fascinating source of phenomena in the physics of light and display deep similarities to their close relatives, quantized vortices in superfluids and Bose-Einstein condensates. The present paper is concerned with the existence of stationary optical vortices wave solutions of nonlinear Schrodinger equations in R-2. For the self-focusing case, we consider three types of problems. The first type concerns the existence of positive radial solutions obtained by a constrained minimization approach. The second type addresses the existence of saddle-point solutions through a mini-max method. As to the third type, we use the variational argument and Nehari manifold to establish nodal solutions. On the other hand, for the defocusing case, we also prove the existence of solutions by constructing approximate sequences of solutions to overcome the loss of compactness. Moreover, in both cases, some non-existence results are discussed as well. (C) 2019 Elsevier Ltd. All rights reserved.
KeywordOptical vortices Variational methods Concentration compactness Nodal solutions
Funding ProjectNNSF of China[11771469] ; Chinese Academy of Sciences[QYZDJ-SSW-SYS021]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000477783900006
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Document Type期刊论文
Corresponding AuthorLi, Hang
Affiliation1.Minzu Univ China, Coll Sci, Beijing, Peoples R China
2.Chinese Acad Sci, AMSS, Inst Appl Math, Beijing 100190, Peoples R China
3.Univ Chinese Acad Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Guo, Qing,Cao, Daomin,Li, Hang. Existence of optical vortices in R-2[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,2019,50:67-85.
APA Guo, Qing,Cao, Daomin,&Li, Hang.(2019).Existence of optical vortices in R-2.NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS,50,67-85.
MLA Guo, Qing,et al."Existence of optical vortices in R-2".NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS 50(2019):67-85.
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