{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T05:10:22Z","timestamp":1775538622661,"version":"3.50.1"},"reference-count":29,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T00:00:00Z","timestamp":1723507200000},"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":["12071432"],"award-info":[{"award-number":["12071432"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LZ24A010007"],"award-info":[{"award-number":["LZ24A010007"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["LY18A010033"],"award-info":[{"award-number":["LY18A010033"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["12071432"],"award-info":[{"award-number":["12071432"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["LZ24A010007"],"award-info":[{"award-number":["LZ24A010007"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100004731","name":"Zhejiang Provincial Natural Science Foundation","doi-asserted-by":"publisher","award":["LY18A010033"],"award-info":[{"award-number":["LY18A010033"]}],"id":[{"id":"10.13039\/501100004731","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Up to now, many works have been conducted to deal with the rational solutions for the autonomous discrete integrable systems, while there have been few works on the rational solutions to the nonautonomous discrete integrable systems. In this paper, we investigate two nonautonomous lattice Korteweg\u2013de Vries type equations: nonautonomous lattice potential Korteweg\u2013de Vries equation and nonautonomous lattice potential modified Korteweg\u2013de Vries equation. By the bilinear method, we construct the rational solutions for the aforesaid equations. These solutions are presented in terms of the Casoratian. By setting special forms of the lattice parameters of the nonautonomous lattice potential Korteweg\u2013de Vries equation, dynamical behaviors for the first two rational solutions of this equation are analyzed with graphical illustration.<\/jats:p>","DOI":"10.3390\/sym16081037","type":"journal-article","created":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T10:54:54Z","timestamp":1723546494000},"page":"1037","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["Rational Solutions for Two Nonautonomous Lattice Korteweg\u2013de Vries Type Equations"],"prefix":"10.3390","volume":"16","author":[{"given":"Mingyu","family":"Ma","sequence":"first","affiliation":[{"name":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3726-1365","authenticated-orcid":false,"given":"Songlin","family":"Zhao","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"}]},{"given":"Wei","family":"Feng","sequence":"additional","affiliation":[{"name":"Department of Applied Mathematics, Zhejiang University of Technology, Hangzhou 310023, China"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"373","DOI":"10.1016\/j.physa.2003.09.020","article-title":"Complete integrability and singularity confinement of nonautonomous modified Korteweg\u2013de Vries and sine-Gordon mappings","volume":"330","author":"Sahadevan","year":"2003","journal-title":"Phys. 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