Some invariant solutions and conservation laws of a type of long-water wave system
Abstract We propose a generalized long-water wave system that reduces to the standard water wave system. We also obtain the Lax pair and symmetries of the generalized shallow-water wave system and single out some their similarity reductions, group-invariant solutions, and series solutions. We furthe...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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SpringerOpen
2019-12-01
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| Series: | Advances in Difference Equations |
| Subjects: | |
| Online Access: | https://doi.org/10.1186/s13662-019-2422-8 |
| _version_ | 1818722755727589376 |
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| author | Xiangzhi Zhang Yufeng Zhang |
| author_facet | Xiangzhi Zhang Yufeng Zhang |
| author_sort | Xiangzhi Zhang |
| collection | DOAJ |
| description | Abstract We propose a generalized long-water wave system that reduces to the standard water wave system. We also obtain the Lax pair and symmetries of the generalized shallow-water wave system and single out some their similarity reductions, group-invariant solutions, and series solutions. We further investigate the corresponding self-adjointness and the conservation laws of the generalized system. |
| first_indexed | 2024-12-17T20:59:40Z |
| format | Article |
| id | doaj.art-cc955996ad9841a0a4a1d7b7d1039853 |
| institution | Directory Open Access Journal |
| issn | 1687-1847 |
| language | English |
| last_indexed | 2024-12-17T20:59:40Z |
| publishDate | 2019-12-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Advances in Difference Equations |
| spelling | doaj.art-cc955996ad9841a0a4a1d7b7d10398532022-12-21T21:32:47ZengSpringerOpenAdvances in Difference Equations1687-18472019-12-012019111410.1186/s13662-019-2422-8Some invariant solutions and conservation laws of a type of long-water wave systemXiangzhi Zhang0Yufeng Zhang1School of Mathematics, China University of Mining and TechnologySchool of Mathematics, China University of Mining and TechnologyAbstract We propose a generalized long-water wave system that reduces to the standard water wave system. We also obtain the Lax pair and symmetries of the generalized shallow-water wave system and single out some their similarity reductions, group-invariant solutions, and series solutions. We further investigate the corresponding self-adjointness and the conservation laws of the generalized system.https://doi.org/10.1186/s13662-019-2422-8Similarity solutionConservation lawSymmetry |
| spellingShingle | Xiangzhi Zhang Yufeng Zhang Some invariant solutions and conservation laws of a type of long-water wave system Advances in Difference Equations Similarity solution Conservation law Symmetry |
| title | Some invariant solutions and conservation laws of a type of long-water wave system |
| title_full | Some invariant solutions and conservation laws of a type of long-water wave system |
| title_fullStr | Some invariant solutions and conservation laws of a type of long-water wave system |
| title_full_unstemmed | Some invariant solutions and conservation laws of a type of long-water wave system |
| title_short | Some invariant solutions and conservation laws of a type of long-water wave system |
| title_sort | some invariant solutions and conservation laws of a type of long water wave system |
| topic | Similarity solution Conservation law Symmetry |
| url | https://doi.org/10.1186/s13662-019-2422-8 |
| work_keys_str_mv | AT xiangzhizhang someinvariantsolutionsandconservationlawsofatypeoflongwaterwavesystem AT yufengzhang someinvariantsolutionsandconservationlawsofatypeoflongwaterwavesystem |