{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:22:16Z","timestamp":1760235736320,"version":"build-2065373602"},"reference-count":27,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T00:00:00Z","timestamp":1632700800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["No.11971475"],"award-info":[{"award-number":["No.11971475"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Postgraduate Research &amp; Practice Innovation Program of Jiangsu Province","award":["No.KYCX21 2147"],"award-info":[{"award-number":["No.KYCX21 2147"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we adopt two kinds of loop algebras corresponding to the Lie algebra B(0,1) to introduce two line spectral problems with different numbers of even and odd superfunctions. Through generalizing the time evolution \u03bbt to a polynomial of \u03bb, two isospectral-nonisospectral super integrable hierarchies are derived in terms of Tu scheme and zero-curvature equation. Among them, the first super integrable hierarchy is further reduced to generalized Fokker\u2013Plank equation and special bond pricing equation, as well as an explicit super integrable system under the choice of specific parameters. More specifically, a super integrable coupled equation is derived and the corresponding integrable properties are discussed, including the Lie point symmetries and one-parameter Lie symmetry groups as well as group-invariant solutions associated with characteristic equation.<\/jats:p>","DOI":"10.3390\/sym13101797","type":"journal-article","created":{"date-parts":[[2021,9,27]],"date-time":"2021-09-27T23:08:31Z","timestamp":1632784111000},"page":"1797","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Two Isospectral-Nonisospectral Super-Integrable Hierarchies and Related Invariant Solutions"],"prefix":"10.3390","volume":"13","author":[{"given":"Huanhuan","family":"Lu","sequence":"first","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yufeng","family":"Zhang","sequence":"additional","affiliation":[{"name":"School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,27]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"330","DOI":"10.1063\/1.528449","article-title":"The trace identity, a powerful tool for constructing the Hamiltonian structure of integrable systems","volume":"30","author":"Tu","year":"1989","journal-title":"J. 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