Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations
We extend the invariant subspace method (ISM) to a class of Hamilton–Jacobi equations (HJEs) and a family of third-order time-fractional dispersive PDEs with the Caputo fractional derivative in this letter. More precisely, the complete classification is presented for such HJEs that admit invariant s...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2023-03-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2023.1160391/full |
| _version_ | 1797858512036954112 |
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| author | Gaizhu Qu Mengmeng Wang Shoufeng Shen |
| author_facet | Gaizhu Qu Mengmeng Wang Shoufeng Shen |
| author_sort | Gaizhu Qu |
| collection | DOAJ |
| description | We extend the invariant subspace method (ISM) to a class of Hamilton–Jacobi equations (HJEs) and a family of third-order time-fractional dispersive PDEs with the Caputo fractional derivative in this letter. More precisely, the complete classification is presented for such HJEs that admit invariant subspaces governed by solutions of the second-order and third-order linear ordinary differential equations (ODEs). Meanwhile, some concrete equations are derived for the construction of new exact solutions u(x,t)=∑i=1nCi(t)fi(x). Then a set of invariant subspaces of the considered third-order time-fractional non-linear dispersive equations are obtained. Based on the Laplace transform method (LTM) and applying several properties of the well known Mitta-Leffer (ML) function, the different types of explicit solutions of a family of third-order time-fractional dispersive PDEs are finally derived. |
| first_indexed | 2024-04-09T21:14:31Z |
| format | Article |
| id | doaj.art-dd4796cc8fc342f58921a025c0f6c2ff |
| institution | Directory Open Access Journal |
| issn | 2296-424X |
| language | English |
| last_indexed | 2024-04-09T21:14:31Z |
| publishDate | 2023-03-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj.art-dd4796cc8fc342f58921a025c0f6c2ff2023-03-28T13:05:13ZengFrontiers Media S.A.Frontiers in Physics2296-424X2023-03-011110.3389/fphy.2023.11603911160391Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equationsGaizhu Qu0Mengmeng Wang1Shoufeng Shen2School of Mathematics and Physics, Weinan Normal University, Weinan, ChinaDepartment of Mathematics, Hangzhou Zhongce Vocational School Qiantang, Hangzhou, ChinaDepartment of Applied Mathematics, Zhejiang University of Technology, Hangzhou, ChinaWe extend the invariant subspace method (ISM) to a class of Hamilton–Jacobi equations (HJEs) and a family of third-order time-fractional dispersive PDEs with the Caputo fractional derivative in this letter. More precisely, the complete classification is presented for such HJEs that admit invariant subspaces governed by solutions of the second-order and third-order linear ordinary differential equations (ODEs). Meanwhile, some concrete equations are derived for the construction of new exact solutions u(x,t)=∑i=1nCi(t)fi(x). Then a set of invariant subspaces of the considered third-order time-fractional non-linear dispersive equations are obtained. Based on the Laplace transform method (LTM) and applying several properties of the well known Mitta-Leffer (ML) function, the different types of explicit solutions of a family of third-order time-fractional dispersive PDEs are finally derived.https://www.frontiersin.org/articles/10.3389/fphy.2023.1160391/fullexact solutionHamilton–Jacobi equationcomplete classificationinvariant subspace methodLaplace transform |
| spellingShingle | Gaizhu Qu Mengmeng Wang Shoufeng Shen Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations Frontiers in Physics exact solution Hamilton–Jacobi equation complete classification invariant subspace method Laplace transform |
| title | Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations |
| title_full | Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations |
| title_fullStr | Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations |
| title_full_unstemmed | Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations |
| title_short | Applications of the invariant subspace method on searching explicit solutions to certain special-type non-linear evolution equations |
| title_sort | applications of the invariant subspace method on searching explicit solutions to certain special type non linear evolution equations |
| topic | exact solution Hamilton–Jacobi equation complete classification invariant subspace method Laplace transform |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2023.1160391/full |
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