A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations

doi:10.1016/j.aml.2017.12.007

CSpace > 系统科学研究所

	A novel hierarchy of two-family-parameter equations: Local, nonlocal, and mixed-local-nonlocal vector nonlinear Schrodinger equations
	Yan, Zhenya1,2
	2018-05-01
发表期刊	APPLIED MATHEMATICS LETTERS
ISSN	0893-9659
卷号	79 页码:123-130
摘要	We 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.
关键词	Two families of parameters Local, nonlocal, and mixed-local-nonlocal VNLS equations Lax pair Conservation laws PT symmetry Symmetry reductions
DOI	10.1016/j.aml.2017.12.007
语种	英语
资助项目	NSFC[11571346] ; NSFC[11731014]
WOS研究方向	Mathematics
WOS类目	Mathematics, Applied
WOS记录号	WOS:000424179500019
出版者	PERGAMON-ELSEVIER SCIENCE LTD
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/29591
专题	系统科学研究所
通讯作者	Yan, Zhenya
作者单位	1.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
推荐引用方式 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.