{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,9]],"date-time":"2024-08-09T00:02:08Z","timestamp":1723161728783},"reference-count":0,"publisher":"Wiley","issue":"70","license":[{"start":{"date-parts":[[2000,1,1]],"date-time":"2000-01-01T00:00:00Z","timestamp":946684800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["International Journal of Mathematics and Mathematical Sciences"],"published-print":{"date-parts":[[2004,1]]},"abstract":"<jats:p>The Kuramoto\u2010Sivashinsky (KS) equation\nis known as a popular prototype to represent a system in which\nthe transport of energy through nonlinear mode coupling produces a\nbalance between long wavelength instability and short\nwavelength dissipation. Existing numerical results indicate that\nthe KS equation admits three classes (namely,\nregular shock, oscillatory shock, and solitary wave) of\nnonperiodic traveling wave solutions and families of multiple\nsolutions in each class. However, the details of multiple\nsolutions are still unclear because of numerical accuracy. In\nthis work, a rational spectral approach is used to compute these\nmultiple traveling wave solutions. Owing to the high accuracy of\nthe employed method, the new families of regular shock waves are\nfound and the fine structure of each family is recognized.<\/jats:p>","DOI":"10.1155\/s0161171204405456","type":"journal-article","created":{"date-parts":[[2004,12,26]],"date-time":"2004-12-26T12:05:25Z","timestamp":1104062725000},"page":"3839-3848","update-policy":"http:\/\/dx.doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multiplicity and structures for traveling wave solutions of the Kuramoto\u2010Sivashinsky equation"],"prefix":"10.1155","volume":"2004","author":[{"given":"Bao-Feng","family":"Feng","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2004,12,26]]},"container-title":["International Journal of Mathematics and Mathematical Sciences"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/downloads.hindawi.com\/journals\/ijmms\/2004\/389587.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1155\/S0161171204405456","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,8,8]],"date-time":"2024-08-08T10:24:22Z","timestamp":1723112662000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1155\/S0161171204405456"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,1]]},"references-count":0,"journal-issue":{"issue":"70","published-print":{"date-parts":[[2004,1]]}},"alternative-id":["10.1155\/S0161171204405456"],"URL":"https:\/\/doi.org\/10.1155\/s0161171204405456","archive":["Portico"],"relation":{},"ISSN":["0161-1712","1687-0425"],"issn-type":[{"type":"print","value":"0161-1712"},{"type":"electronic","value":"1687-0425"}],"subject":[],"published":{"date-parts":[[2004,1]]},"assertion":[{"value":"2004-05-06","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2004-12-26","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}