{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,2,21]],"date-time":"2025-02-21T10:42:23Z","timestamp":1740134543628,"version":"3.37.3"},"reference-count":28,"publisher":"Wiley","license":[{"start":{"date-parts":[[2013,1,1]],"date-time":"2013-01-01T00:00:00Z","timestamp":1356998400000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["11171115","S2012040007959","2012ZM0057"],"award-info":[{"award-number":["11171115","S2012040007959","2012ZM0057"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003453","name":"Natural Science Foundation of Guangdong Province","doi-asserted-by":"crossref","award":["11171115","S2012040007959","2012ZM0057"],"award-info":[{"award-number":["11171115","S2012040007959","2012ZM0057"]}],"id":[{"id":"10.13039\/501100003453","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["11171115","S2012040007959","2012ZM0057"],"award-info":[{"award-number":["11171115","S2012040007959","2012ZM0057"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2013]]},"abstract":"<jats:p>The objective of this paper is to extend some results of pioneers for the nonlinear equation<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M1\"><mml:mrow><mml:msub><mml:mi>m<\/mml:mi><mml:mi>t<\/mml:mi><\/mml:msub><mml:mo>=<\/mml:mo><mml:mrow><mml:mn>(1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mn>2)<\/mml:mn><\/mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mrow><mml:msup><mml:mi>m<\/mml:mi><mml:mi>k<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:mrow><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mrow><mml:mi>x<\/mml:mi><mml:mi>x<\/mml:mi><mml:mi>x<\/mml:mi><\/mml:mrow><\/mml:msub><mml:mo>\u2212<\/mml:mo><mml:mrow><mml:mn>(1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mn>2)<\/mml:mn><\/mml:mrow><mml:msub><mml:mrow><mml:mrow><mml:mo stretchy=\"false\">(<\/mml:mo><mml:mrow><mml:mrow><mml:mn>1<\/mml:mn><mml:mo>\/<\/mml:mo><mml:mrow><mml:msup><mml:mi>m<\/mml:mi><mml:mi>k<\/mml:mi><\/mml:msup><\/mml:mrow><\/mml:mrow><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><mml:mi>x<\/mml:mi><\/mml:msub><\/mml:mrow><\/mml:math>introduced by Qiao. The equivalent relationship of the traveling wave solutions between the integrable equation and the generalized KdV equation is revealed. Moreover, when<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M2\"><mml:mrow><mml:mi>k<\/mml:mi><mml:mo>=<\/mml:mo><mml:mo>\u2212<\/mml:mo><mml:mrow><mml:mi>(p<\/mml:mi><mml:mo>\/<\/mml:mo><mml:mi>q)<\/mml:mi><\/mml:mrow><mml:mrow><mml:mo>\u2009\u2009(<\/mml:mo><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>\u2260<\/mml:mo><mml:mi>q<\/mml:mi><\/mml:mrow><\/mml:mrow><\/mml:mrow><\/mml:math>and<mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\" id=\"M3\"><mml:mrow><mml:mrow><mml:mrow><mml:mi>p<\/mml:mi><mml:mo>,<\/mml:mo><mml:mi>q<\/mml:mi><mml:mo>\u2208<\/mml:mo><mml:msup><mml:mi>\u2124<\/mml:mi><mml:mo>+<\/mml:mo><\/mml:msup><\/mml:mrow><mml:mo stretchy=\"false\">)<\/mml:mo><\/mml:mrow><\/mml:mrow><\/mml:math>, we obtain some explicit traveling wave solutions by the bifurcation method of dynamical systems.<\/jats:p>","DOI":"10.1155\/2013\/681383","type":"journal-article","created":{"date-parts":[[2013,3,20]],"date-time":"2013-03-20T21:01:20Z","timestamp":1363813280000},"page":"1-6","source":"Crossref","is-referenced-by-count":3,"title":["Further Results on the Traveling Wave Solutions for an Integrable Equation"],"prefix":"10.1155","volume":"2013","author":[{"given":"Chaohong","family":"Pan","sequence":"first","affiliation":[{"name":"Department of Mathematics, South China University of Technology, Guangzhou 510640, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhengrong","family":"Liu","sequence":"additional","affiliation":[{"name":"Department of Mathematics, South China University of Technology, Guangzhou 510640, 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