{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:42:29Z","timestamp":1777704149853,"version":"3.51.4"},"reference-count":25,"publisher":"SAGE Publications","issue":"3","license":[{"start":{"date-parts":[[2020,1,30]],"date-time":"2020-01-30T00:00:00Z","timestamp":1580342400000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"published-print":{"date-parts":[[2020,3,4]]},"abstract":"<jats:p>\n                    This research paper studies the soliton waves of the (\n                    <jats:italic>N<\/jats:italic>\n                    \u200a+\u200a1) dimensional time-fractional conformable Sinh-Gordon equation by the implementation of the modified Khater method. This equation studies surfaces of constant negative curvature, such as the Gauss-Codazzi equation for surfaces of curvature. Using the Painlev\u00e9 property is employed to support the modified Khater method in formulating of abundant traveling wave solutions. The performance of the used technique emphasizes the power, effect, and ability for applying to many nonlinear evolution equations.\n                  <\/jats:p>","DOI":"10.3233\/jifs-179560","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T11:31:40Z","timestamp":1580470300000},"page":"2745-2752","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":13,"title":["Ample soliton waves for the crystal lattice formation of the conformable time-fractional (N\u200a+\u200a1) Sinh-Gordon equation by the modified Khater method and the Painlev\u00e9 property"],"prefix":"10.1177","volume":"38","author":[{"given":"Haiyong","family":"Qin","sequence":"first","affiliation":[{"name":"School of Control Science and Engineering, Shandong University, Jinan, Shandong, China"},{"name":"School of Mathematics, Qilu Normal University, Jinan, Shandong Province, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Raghda A.M.","family":"Attia","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jiangsu University, China"},{"name":"Department of Basic Science, 10th Higher Technological Institute, Ramadan, Egypt"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mostafa M.A.","family":"Khater","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jiangsu University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dianchen","family":"Lu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Faculty of Science, Jiangsu University, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2020,1,30]]},"reference":[{"issue":"4","key":"e_1_3_2_2_2","article-title":"\u201cOn the New Solitary Wave Solution of the Generalized HirotaSatsuma Couple KdV System,\u201d","volume":"15","author":"Khater M.M.A.","year":"2015","unstructured":"KhaterM.M.A., \u201cOn the New Solitary Wave Solution of the Generalized HirotaSatsuma Couple KdV System,\u201d Glob. 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