{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,15]],"date-time":"2026-04-15T23:08:51Z","timestamp":1776294531048,"version":"3.50.1"},"reference-count":24,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T00:00:00Z","timestamp":1742256000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"National Natural Science Foundation of China","award":["12371256"],"award-info":[{"award-number":["12371256"]}]},{"name":"National Natural Science Foundation of China","award":["11971475"],"award-info":[{"award-number":["11971475"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>A new generalized (3+1)-dimensional Kadomtsev\u2013Petviashvil (3dKP) equation is derived from the inverse scattering transform method. This equation can be reduced to the standard KP equation and the well-know (3+1)-dimensional equation. In making use of the Lax pair transformation, a B\u00e4cklund transformation of the generalized (3+1)-dimensional KP equation is constructed and some soliton solutions are produced. Finally, a superposition formula is singled out as well by making use of the B\u00e4cklund transformation. As far as we know, the work presented in this paper has not been studied up to now.<\/jats:p>","DOI":"10.3390\/axioms14030225","type":"journal-article","created":{"date-parts":[[2025,3,18]],"date-time":"2025-03-18T10:43:51Z","timestamp":1742294631000},"page":"225","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["B\u00e4cklund Transformation for Solving a (3+1)-Dimensional Integrable Equation"],"prefix":"10.3390","volume":"14","author":[{"given":"Binlu","family":"Feng","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Weifang University, Weifang 261061, China"},{"name":"College of Technology and Data, Yantai Nanshan University, Yantai 265713, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Linlin","family":"Gui","sequence":"additional","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"}]},{"given":"Siqi","family":"Han","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":[[2025,3,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"925","DOI":"10.1103\/PhysRevLett.33.925","article-title":"General Derivation of B\u00e4cklund transformations from Inverse Scattering Problems","volume":"57","author":"Chen","year":"1974","journal-title":"Phys. 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