All meromorphic solutions for two forms of odd order algebraic differential equations and its applications
In this article, 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 two classes of odd order algebraic differential equations with the weak 〈 p...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Elsevier Inc.
2014
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| Subjects: | |
| Online Access: | http://hdl.handle.net/20.500.11937/30020 |
| _version_ | 1848752967650377728 |
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| author | Yuan, W. Wu, Yong Hong Chen, Q. Huang, Y. |
| author_facet | Yuan, W. Wu, Yong Hong Chen, Q. Huang, Y. |
| author_sort | Yuan, W. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | In this article, 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 two classes 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 some generalized Bretherton equations 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, and using the traveling wave nobody can find other new exact solutions for many nonlinear partial differential equations by any method. |
| first_indexed | 2025-11-14T08:17:02Z |
| format | Journal Article |
| id | curtin-20.500.11937-30020 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T08:17:02Z |
| publishDate | 2014 |
| publisher | Elsevier Inc. |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-300202017-09-13T15:29:12Z All meromorphic solutions for two forms of odd order algebraic differential equations and its applications Yuan, W. Wu, Yong Hong Chen, Q. Huang, Y. Exact solution Meromorphic function Elliptic function Differential equation In this article, 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 two classes 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 some generalized Bretherton equations 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, and using the traveling wave nobody can find other new exact solutions for many nonlinear partial differential equations by any method. 2014 Journal Article http://hdl.handle.net/20.500.11937/30020 10.1016/j.amc.2014.04.099 Elsevier Inc. restricted |
| spellingShingle | Exact solution Meromorphic function Elliptic function Differential equation Yuan, W. Wu, Yong Hong Chen, Q. Huang, Y. All meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| title | All meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| title_full | All meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| title_fullStr | All meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| title_full_unstemmed | All meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| title_short | All meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| title_sort | all meromorphic solutions for two forms of odd order algebraic differential equations and its applications |
| topic | Exact solution Meromorphic function Elliptic function Differential equation |
| url | http://hdl.handle.net/20.500.11937/30020 |