The representation of meromorphic solutions for a class of odd order algebraic differential equations and its applications |
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| Authors: | Zifeng Huang Liming Zhang Qiuhui Chen Wenjun Yuan |
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| Institution: | 1. School of Mathematics and Information Science, Guangzhou University, , Guangzhou 510006, China;2. Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes, Guangzhou University, , Guangzhou 510006, China;3. Faculty of Science and Technology, University of Macau, , Macau 3001, China;4. Cisco School of Informatics, Guangdong University of Foreign Studies, , Guangzhou 510420, China |
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| Abstract: | In this paper, we employ the Nevanlinna's value distribution theory to investigate the existence of meromorphic solutions of algebraic differential equations. We obtain the representations of all meromorphic solutions for a class of odd order algebraic differential equations with the weak ?p,q?and dominant conditions. Moreover, we give the complex method to find all traveling wave exact solutions of corresponding partial differential equations. As an example, we obtain all meromorphic solutions of the Kuramoto–Sivashinsky equation by using our complex method. Our results show that the complex method provides a powerful mathematical tool for solving great many nonlinear partial differential equations in mathematical physics. Copyright © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | differential equation exact solution meromorphic function elliptic function |
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