{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:05:28Z","timestamp":1760241928922,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,23]],"date-time":"2018-10-23T00:00:00Z","timestamp":1540252800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>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 schr\u00f6dinger 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    \u03c4   -symmetries are generated from the nonisospectral hierarchy and form an infinite-dimensional symmetry algebra with the K-symmetries.<\/jats:p>","DOI":"10.3390\/sym10110535","type":"journal-article","created":{"date-parts":[[2018,10,24]],"date-time":"2018-10-24T02:59:40Z","timestamp":1540349980000},"page":"535","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A \u03c4-Symmetry Algebra of the Generalized Derivative Nonlinear Schr\u00f6dinger Soliton Hierarchy with an Arbitrary Parameter"],"prefix":"10.3390","volume":"10","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8180-4814","authenticated-orcid":false,"given":"Jian-bing","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China"}]},{"given":"Yingyin","family":"Gongye","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Jiangsu Normal University, Xuzhou 221116, Jiangsu, China"}]},{"given":"Wen-Xiu","family":"Ma","sequence":"additional","affiliation":[{"name":"Department of Mathematics and Statistics, University of South Florida, Tampa, FL 33620, USA"},{"name":"College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, Shandong, China"},{"name":"Department of Mathematical Sciences, North-West University, Mafikeng Campus, Mmabatho 2735, South Africa"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1002\/sapm1974534249","article-title":"The Inverse Scattering Transform-Fourier Analysis for Nonlinear Problems","volume":"53","author":"Ablowitz","year":"1974","journal-title":"Stud. 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