New solutions to a category of nonlinear PDEs
The nonlinear partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain nonlinear partial differential equation, the extended hyperbolic auxiliary equation method (EHAEM) is introduced in this...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2025-01-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2025.1547245/full |
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| author | Bacui Li Fuzhang Wang |
| author_facet | Bacui Li Fuzhang Wang |
| author_sort | Bacui Li |
| collection | DOAJ |
| description | The nonlinear partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain nonlinear partial differential equation, the extended hyperbolic auxiliary equation method (EHAEM) is introduced in this article by means of the symbolic computation software. The basic idea of the new algorithm is that if certain nonlinear partial differential equation can be converted into the form of elliptic equation, then its solutions are readily obtained. By taking the generalized Schrödinger equation as an example, we demonstrate the effectiveness of the proposed algorithm. Meanwhile, many new solutions are worked out, which may be useful for depicting nonlinear physical phenomena. |
| format | Article |
| id | doaj-art-185ac83fc129445e95b56313749832cc |
| institution | Kabale University |
| issn | 2296-424X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj-art-185ac83fc129445e95b56313749832cc2025-01-30T05:10:44ZengFrontiers Media S.A.Frontiers in Physics2296-424X2025-01-011310.3389/fphy.2025.15472451547245New solutions to a category of nonlinear PDEsBacui Li0Fuzhang Wang1Scientific Research Department, Party School of CPC Fushun, Fushun, ChinaInstitute of Data Science and Engineering, Xuzhou University of Technology, Xuzhou, ChinaThe nonlinear partial differential equations are not only used in many physical models, but also fundamentally applied in the field of nonlinear science. In order to solve certain nonlinear partial differential equation, the extended hyperbolic auxiliary equation method (EHAEM) is introduced in this article by means of the symbolic computation software. The basic idea of the new algorithm is that if certain nonlinear partial differential equation can be converted into the form of elliptic equation, then its solutions are readily obtained. By taking the generalized Schrödinger equation as an example, we demonstrate the effectiveness of the proposed algorithm. Meanwhile, many new solutions are worked out, which may be useful for depicting nonlinear physical phenomena.https://www.frontiersin.org/articles/10.3389/fphy.2025.1547245/fullpartial differential equationsolitary wave solutionJacobian elliptic function solutionsymbolic computation softwarecomputerized mechanization |
| spellingShingle | Bacui Li Fuzhang Wang New solutions to a category of nonlinear PDEs Frontiers in Physics partial differential equation solitary wave solution Jacobian elliptic function solution symbolic computation software computerized mechanization |
| title | New solutions to a category of nonlinear PDEs |
| title_full | New solutions to a category of nonlinear PDEs |
| title_fullStr | New solutions to a category of nonlinear PDEs |
| title_full_unstemmed | New solutions to a category of nonlinear PDEs |
| title_short | New solutions to a category of nonlinear PDEs |
| title_sort | new solutions to a category of nonlinear pdes |
| topic | partial differential equation solitary wave solution Jacobian elliptic function solution symbolic computation software computerized mechanization |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2025.1547245/full |
| work_keys_str_mv | AT bacuili newsolutionstoacategoryofnonlinearpdes AT fuzhangwang newsolutionstoacategoryofnonlinearpdes |