Conserved quantities and solutions of a -dimensional H a ˇ r a ˇ gus-Courcelle-Il’ichev model

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• 作者：Abdullahi Rashid Adem ^{Abdullahi.Adem@nwu.ac.za" class="auth_mail" title="E-mail the corresponding author} ; Chaudry Masood Khalique ; ^{Masood.Khalique@nwu.ac.za" class="auth_mail" title="E-mail the corresponding author}
• 关键词：(2+1)(2+1)-dimensional Haˇraˇgus-Courcelle&ndash ; Il&rsquo ; ichev equation model ; Conservation laws ; Lie symmetry methods ; Auxiliary equation method
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：71
• 期：5
• 页码：1129-1136
• 全文大小：653 K

文摘

In this paper we study a class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116300177&_mathId=si1.gif&_user=111111111&_pii=S0898122116300177&_rdoc=1&_issn=08981221&md5=43c5b3226b911178ed6647a79561d7b7" title="Click to view the MathML source">(2+1)class="mathContainer hidden">class="mathCode">$(2+1)$-dimensional Haˇraˇgus-Courcelle–Il’ichev equation (HCI) that models gravity–capillary and flexural-gravity waves. This equation is a generalization of the Kadomtsev–Petviashvili equation, and is obtained due to the presence of certain surface effects. We obtain analytic solutions of the HCI equation by using the Lie symmetry method along with the auxiliary equation method. The solutions obtained are the solitary, cnoidal and snoidal wave solutions. In addition to this we derive the conservation laws of the underlying equation by using the multiplier approach.