Bibliographic Details
| Title: |
All Traveling Wave Exact Solutions of the Kawahara Equation Using the Complex Method |
| Authors: |
Feng Ye, Jian Tian, Xiaoting Zhang, Chunling Jiang, Tong Ouyang, Yongyi Gu |
| Source: |
Axioms, Vol 11, Iss 7, p 330 (2022) |
| Publisher Information: |
MDPI AG, 2022. |
| Publication Year: |
2022 |
| Collection: |
LCC:Mathematics |
| Subject Terms: |
Kawahara equation, complex method, exact solution, elliptic function, Mathematics, QA1-939 |
| More Details: |
In this article, we prove that the ⟨p,q⟩ condition holds, first by using the Fuchs index of the complex Kawahara equation, and then proving that all meromorphic solutions of complex Kawahara equations belong to the class W. Moreover, the complex method is employed to get all meromorphic solutions of complex Kawahara equation and all traveling wave exact solutions of Kawahara equation. Our results reveal that all rational solutions ur(x+νt) and simply periodic solutions us,1(x+νt) of Kawahara equation are solitary wave solutions, while simply periodic solutions us,2(x+νt) are not real-valued. Finally, computer simulations are given to demonstrate the main results of this paper. At the same time, we believe that this method is a very effective and powerful method of looking for exact solutions to the mathematical physics equations, and the search process is simpler than other methods. |
| Document Type: |
article |
| File Description: |
electronic resource |
| Language: |
English |
| ISSN: |
2075-1680 |
| Relation: |
https://www.mdpi.com/2075-1680/11/7/330; https://doaj.org/toc/2075-1680 |
| DOI: |
10.3390/axioms11070330 |
| Access URL: |
https://doaj.org/article/8b677eeafbe04f33a9f02bc15b691d50 |
| Accession Number: |
edsdoj.8b677eeafbe04f33a9f02bc15b691d50 |
| Database: |
Directory of Open Access Journals |
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