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A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations
Yan, Zhenya1,2
2018-05-01
Source PublicationAPPLIED MATHEMATICS LETTERS
ISSN0893-9659
Volume79Pages:123-130
AbstractWe use two families of parameters {(epsilon(xj), epsilon(tj)) vertical bar epsilon(xj), t(j) = +/- 1, j = 1, 2, ... , n} to first introduce a unified novel hierarchy of two-family-parameter equations (simply called Q(epsilon x (n) over bar,epsilon t (n) over bar)((n)) hierarchy), connecting integrable local, nonlocal, novel mixed-local-nonlocal, and other nonlocal vector nonlinear Schrodinger (VNLS) equations. The Q(epsilon x (n) over bar,epsilon t (n) over bar)((n)) system with (epsilon(xj), epsilon(tj)) = (+/- 1,1), j = 1, 2, ... , n is shown to possess Lax parrs and infinite number of conservation laws. Moreover, we also analyze the PT symmetry of the Hamiltonians with self-induced potentials. The multi-linear forms and some symmetry reductions are also studied. In fact, the used two families of parameters can also be extended to the general case {(epsilon(xj), epsilon(tj))vertical bar epsilon(xj) = e(i theta xj) , epsilon(tj) = e(i theta tj) , theta(xj) , theta(tj) is an element of[0, 2 pi), j = 1, 2, ... , n} to generate more types of nonlinear equations. The novel two-family-parameter (or multi-family-parameter for higher-dimensional cases) idea can also be applied to other local nonlinear evolution equations to find novel integrable and non-integrable nonlocal and mixed-local-nonlocal systems. (C) 2017 Elsevier Ltd. All rights reserved.
KeywordTwo families of parameters Local, nonlocal, and mixed-local-nonlocal VNLS equations Lax pair Conservation laws PT symmetry Symmetry reductions
DOI10.1016/j.aml.2017.12.007
Language英语
Funding ProjectNSFC[11571346] ; NSFC[11731014]
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000424179500019
PublisherPERGAMON-ELSEVIER SCIENCE LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/29591
Collection系统科学研究所
Affiliation1.Chinese Acad Sci, Acad Math & Syst Sci, Key Lab Math Mech, Beijing 100190, Peoples R China
2.Univ Chinese Acad Sci, Sch Math Sci, Beijing 100049, Peoples R China
Recommended Citation
GB/T 7714
Yan, Zhenya. A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations[J]. APPLIED MATHEMATICS LETTERS,2018,79:123-130.
APA Yan, Zhenya.(2018).A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations.APPLIED MATHEMATICS LETTERS,79,123-130.
MLA Yan, Zhenya."A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations".APPLIED MATHEMATICS LETTERS 79(2018):123-130.
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