Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion
The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi’s ell...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-05-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/15/5/1021 |
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| author | Xiaohua Zeng Xiling Wu Changzhou Liang Chiping Yuan Jieping Cai |
| author_facet | Xiaohua Zeng Xiling Wu Changzhou Liang Chiping Yuan Jieping Cai |
| author_sort | Xiaohua Zeng |
| collection | DOAJ |
| description | The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi’s elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>→</mo><mn>1</mn></mrow></semantics></math></inline-formula>, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained. |
| first_indexed | 2024-03-11T03:16:39Z |
| format | Article |
| id | doaj.art-b5dd94e65f374c74854d765ac2640f66 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-11T03:16:39Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-b5dd94e65f374c74854d765ac2640f662023-11-18T03:29:49ZengMDPI AGSymmetry2073-89942023-05-01155102110.3390/sym15051021Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function ExpansionXiaohua Zeng0Xiling Wu1Changzhou Liang2Chiping Yuan3Jieping Cai4School of Economics and Trade, Guangzhou Xinhua University, Dongguan 523133, ChinaSchool of Economics and Trade, Guangzhou Xinhua University, Dongguan 523133, ChinaSchool of Economics and Trade, Guangzhou Xinhua University, Dongguan 523133, ChinaInstitute of Guangdong, Hong Kong and Macao Development Studies, Sun Yat-sen University, Guangzhou 510275, ChinaSchool of Economics and Trade, Guangzhou Xinhua University, Dongguan 523133, ChinaThe exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi’s elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>m</mi><mo>→</mo><mn>1</mn></mrow></semantics></math></inline-formula>, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained.https://www.mdpi.com/2073-8994/15/5/1021coupled KdV equationsvariable coefficientsquadratic Jacobi’s elliptic functionsolitontraveling wave solution |
| spellingShingle | Xiaohua Zeng Xiling Wu Changzhou Liang Chiping Yuan Jieping Cai Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion Symmetry coupled KdV equations variable coefficients quadratic Jacobi’s elliptic function soliton traveling wave solution |
| title | Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion |
| title_full | Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion |
| title_fullStr | Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion |
| title_full_unstemmed | Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion |
| title_short | Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion |
| title_sort | exact solutions for coupled variable coefficient kdv equation via quadratic jacobi s elliptic function expansion |
| topic | coupled KdV equations variable coefficients quadratic Jacobi’s elliptic function soliton traveling wave solution |
| url | https://www.mdpi.com/2073-8994/15/5/1021 |
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