Rational solutions for a -dimensional nonlinear model in water waves generated by the Jaulent-Miodek hierarchy

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• 作者：Jin-Wei Yang ; Yi-Tian Gao ; ^{gaoyt163@163.com" class="auth_mail" title="E-mail the corresponding author} ; Chuan-Qi Su ; Chen Zhao ; Yu-Jie Feng
• 关键词：Nonlinear water waves ; Nonlinear evolution equation ; Jaulent&ndash ; Miodek hierarchy ; Rational solutions ; Hirota&rsquo ; s bilinear method ; Pfaffian
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：72
• 期：11
• 页码：2685-2693
• 全文大小：1271 K

文摘

This paper deals with a (2+1)$(2+1)$-dimensional nonlinear evolution equation (NLEE) generated by the Jaulent–Miodek hierarchy for nonlinear water waves via the Hirota’s bilinear method and Pfaffian. First, we construct rational solutions for general bilinear equations, and then convert the target bilinear equations to the general ones to obtain their rational solutions. The Pfaffian plays a role to simplifying the computations compared with the determinant way in the existing literatures. Once the first- and second-order rational solutions have been obtained, the higher-order solutions can be derived by the same token. Figures for the first- and second-order rational solutions are plotted and analyzed. As an application, the rational solutions for the modified Kadomtsev–Petviashvili equation have also been constructed. The method might be used for some other NLEEs to construct their rational solutions.