Document Type
Article
Publication Date
10-2018
Keywords
generalized derivative nonlinear shcrödinger equation, master symmetry, infinite- dimensional Lie algebra
Digital Object Identifier (DOI)
https://doi.org/10.3390/sym10110535
Abstract
A matrix spectral problem is researched with an arbitrary parameter. Through zero curvature equations, two hierarchies are constructed of isospectral and nonisospectral generalized derivative nonlinear schrödinger equations. The resulting hierarchies include the Kaup-Newell equation, the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation, the modified Korteweg-de Vries equation, the Sharma-Tasso-Olever equation and a new equation as special reductions. The integro-differential operator related to the isospectral and nonisospectral hierarchies is shown to be not only a hereditary but also a strong symmetry of the whole isospectral hierarchy. For the isospectral hierarchy, the corresponding τ -symmetries are generated from the nonisospectral hierarchy and form an infinite-dimensional symmetry algebra with the K-symmetries.
Rights Information
This work is licensed under a Creative Commons Attribution 4.0 License.
Was this content written or created while at USF?
Yes
Citation / Publisher Attribution
Symmetry, v. 10, issue 11, art. 535
Scholar Commons Citation
Zhang, Jian-bing; Gongye, Yingyin; and Ma, Wen-Xiu, "A τ-Symmetry Algebra of the Generalized Derivative Nonlinear Schrödinger Soliton Hierarchy with an Arbitrary Parameter" (2018). Mathematics and Statistics Faculty Publications. 26.
https://digitalcommons.usf.edu/mth_facpub/26
