{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,19]],"date-time":"2025-10-19T16:05:45Z","timestamp":1760889945258,"version":"build-2065373602"},"reference-count":34,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T00:00:00Z","timestamp":1572825600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Yufeng Zhang","award":["No.2017XKZD11"],"award-info":[{"award-number":["No.2017XKZD11"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>In this article, we construct a new strongly coupled Boussinesq\u2013Burgers system taking values in a commutative subalgebra     Z 2    . A residual symmetry of the strongly coupled Boussinesq\u2013Burgers system is achieved by a given truncated Painlev\u00e9 expansion. The residue symmetry with respect to the singularity manifold is a nonlocal symmetry. Then, we introduce a suitable enlarged system to localize the nonlocal residual symmetry. In addition, a B\u00e4cklund transformation is obtained with the help of Lie\u2019s first theorem. Further, the linear superposition of multiple residual symmetries is localized to a Lie point symmetry, and a N-th B\u00e4cklund transformation is also obtained.<\/jats:p>","DOI":"10.3390\/sym11111365","type":"journal-article","created":{"date-parts":[[2019,11,4]],"date-time":"2019-11-04T04:13:08Z","timestamp":1572840788000},"page":"1365","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Residual Symmetries and B\u00e4cklund Transformations of Strongly Coupled Boussinesq\u2013Burgers System"],"prefix":"10.3390","volume":"11","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1058-7111","authenticated-orcid":false,"given":"Haifeng","family":"Wang","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":[[2019,11,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1095","DOI":"10.1103\/PhysRevLett.19.1095","article-title":"Method for solving the Korteweg-de Vries equation","volume":"19","author":"Gardner","year":"1967","journal-title":"Phys. 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