The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation
Due to the importance of the nonlinear partial differential equations in applied physics and engineering, many mathematicians and physicists are interesting to the nonlinear partial differential equations. One of the main tasks of studying the nonlinear partial differential equations is to obtain th...
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| Format: | Article |
| Language: | English |
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Elsevier
2024-03-01
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| Series: | Results in Physics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379724001888 |
| _version_ | 1827316581157306368 |
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| author | Jianping Li Can Xu Junliang Lu |
| author_facet | Jianping Li Can Xu Junliang Lu |
| author_sort | Jianping Li |
| collection | DOAJ |
| description | Due to the importance of the nonlinear partial differential equations in applied physics and engineering, many mathematicians and physicists are interesting to the nonlinear partial differential equations. One of the main tasks of studying the nonlinear partial differential equations is to obtain the exact solutions for the nonlinear partial differential equations. In this paper, we study the exact solutions of a generalized (2+1)-dimensional nonlinear partial differential equation. According to the modified hyperbolic function method and the traveling transformation method, the generalized (2+1)-dimensional nonlinear partial differential equation is changed into an ordinary differential equation. By taking the homogeneous balance between the highest order nonlinear terms and the highest order derivative terms, we change the differential equation into an algebraic system. By solving the algebraic system, we obtain the solutions for the nonlinear partial differential equation. At last, some solutions and their figures are given by specific parameters. All the solutions conclude the trigonometric function solutions, the positive hyperbolic function solutions, and the hyperbolic trigonometric function solutions. These solutions exhibit the dynamics of nonlinear waves and the solutions are useful for the study on interaction behavior of nonlinear waves in shallow water, plasma, nonlinear optics and Bose–Einstein condensates. |
| first_indexed | 2024-03-07T21:52:56Z |
| format | Article |
| id | doaj.art-0f720a4762dd4471bbdb408330ae2c00 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-04-24T23:18:00Z |
| publishDate | 2024-03-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-0f720a4762dd4471bbdb408330ae2c002024-03-17T07:53:44ZengElsevierResults in Physics2211-37972024-03-0158107506The exact solutions to the generalized (2+1)-dimensional nonlinear wave equationJianping Li0Can Xu1Junliang Lu2School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, PR ChinaSchool of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, PR ChinaCorresponding author.; School of Statistics and Mathematics, Yunnan University of Finance and Economics, Kunming, 650221, PR ChinaDue to the importance of the nonlinear partial differential equations in applied physics and engineering, many mathematicians and physicists are interesting to the nonlinear partial differential equations. One of the main tasks of studying the nonlinear partial differential equations is to obtain the exact solutions for the nonlinear partial differential equations. In this paper, we study the exact solutions of a generalized (2+1)-dimensional nonlinear partial differential equation. According to the modified hyperbolic function method and the traveling transformation method, the generalized (2+1)-dimensional nonlinear partial differential equation is changed into an ordinary differential equation. By taking the homogeneous balance between the highest order nonlinear terms and the highest order derivative terms, we change the differential equation into an algebraic system. By solving the algebraic system, we obtain the solutions for the nonlinear partial differential equation. At last, some solutions and their figures are given by specific parameters. All the solutions conclude the trigonometric function solutions, the positive hyperbolic function solutions, and the hyperbolic trigonometric function solutions. These solutions exhibit the dynamics of nonlinear waves and the solutions are useful for the study on interaction behavior of nonlinear waves in shallow water, plasma, nonlinear optics and Bose–Einstein condensates.http://www.sciencedirect.com/science/article/pii/S2211379724001888Generalized (2+1)-dimensional nonlinear partial differential equationModified hyperbolic function expansion methodTraveling wave solutions |
| spellingShingle | Jianping Li Can Xu Junliang Lu The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation Results in Physics Generalized (2+1)-dimensional nonlinear partial differential equation Modified hyperbolic function expansion method Traveling wave solutions |
| title | The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation |
| title_full | The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation |
| title_fullStr | The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation |
| title_full_unstemmed | The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation |
| title_short | The exact solutions to the generalized (2+1)-dimensional nonlinear wave equation |
| title_sort | exact solutions to the generalized 2 1 dimensional nonlinear wave equation |
| topic | Generalized (2+1)-dimensional nonlinear partial differential equation Modified hyperbolic function expansion method Traveling wave solutions |
| url | http://www.sciencedirect.com/science/article/pii/S2211379724001888 |
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