{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,8]],"date-time":"2025-11-08T12:56:17Z","timestamp":1762606577195,"version":"build-2065373602"},"reference-count":43,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2015,5,13]],"date-time":"2015-05-13T00:00:00Z","timestamp":1431475200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11371071"],"award-info":[{"award-number":["11371071"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"Liaoning BaiQianWan Talents Program","award":["2013921055"],"award-info":[{"award-number":["2013921055"]}]},{"name":"Natural Science Foundation of Educational Committee of Liaoning Province of China","award":["L2012404"],"award-info":[{"award-number":["L2012404"]}]},{"name":"PhD Start-up Fund of Liaoning Province of China","award":["20141137"],"award-info":[{"award-number":["20141137"]}]},{"name":"PhD Start-up Fund of Bohai University","award":["bsqd2013025"],"award-info":[{"award-number":["bsqd2013025"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper, the exp-function method is improved to construct exact solutions of non-linear lattice equations by modifying its exponential function ans\u00e4tz. The improved method has two advantages. One is that it can solve non-linear lattice equations with variable coefficients, and the other is that it is not necessary to balance the highest order derivative with the highest order nonlinear term in the procedure of determining the exponential function ans\u00e4tz. To show the advantages of this improved method, a variable-coefficient mKdV lattice equation is considered. As a result, new exact solutions, which include kink-type solutions and bell-kink-type solutions, are obtained.<\/jats:p>","DOI":"10.3390\/e17053182","type":"journal-article","created":{"date-parts":[[2015,5,13]],"date-time":"2015-05-13T12:42:07Z","timestamp":1431520927000},"page":"3182-3193","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":8,"title":["Exact Solutions of Non-Linear Lattice Equations by an Improved Exp-Function Method"],"prefix":"10.3390","volume":"17","author":[{"given":"Sheng","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, 19 Keji Road, New Songshan District, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jiahong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, 19 Keji Road, New Songshan District, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yingying","family":"Zhou","sequence":"additional","affiliation":[{"name":"School of Mathematics and Physics, Bohai University, 19 Keji Road, New Songshan District, Jinzhou 121013, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2015,5,13]]},"reference":[{"unstructured":"Fermi, E., Pasta, J., and Ulam, S. 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