Symmetry group analysis and invariant solutions of hydrodynamic-type systems
We study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence on t,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these sy...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204206147 |
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| _version_ | 1850179103682985984 |
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| author | M. B. Sheftel |
| author_facet | M. B. Sheftel |
| author_sort | M. B. Sheftel |
| collection | DOAJ |
| description | We study point and higher symmetries of systems of the
hydrodynamic type with and without an explicit dependence on
t,x. We consider such systems which satisfy the existence
conditions for an infinite-dimensional group of hydrodynamic
symmetries which implies linearizing transformations for these
systems. Under additional restrictions on the systems, we obtain
recursion operators for symmetries and use them to construct
infinite discrete sets of exact solutions of the studied
equations. We find the interrelation between higher symmetries and
recursion operators. Two-component systems are studied in more
detail than n-component systems. As a special case, we consider
Hamiltonian and semi-Hamiltonian systems of
Tsarëv. |
| format | Article |
| id | doaj-art-be4376f06fee41e1be107211539ad985 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-be4376f06fee41e1be107211539ad9852025-08-20T02:18:35ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-0120041048753410.1155/S0161171204206147Symmetry group analysis and invariant solutions of hydrodynamic-type systemsM. B. Sheftel0Department of Higher Mathematics, North-Western State Technical University, Millionnaya Street 5, St. Petersburg 191186, RussiaWe study point and higher symmetries of systems of the hydrodynamic type with and without an explicit dependence on t,x. We consider such systems which satisfy the existence conditions for an infinite-dimensional group of hydrodynamic symmetries which implies linearizing transformations for these systems. Under additional restrictions on the systems, we obtain recursion operators for symmetries and use them to construct infinite discrete sets of exact solutions of the studied equations. We find the interrelation between higher symmetries and recursion operators. Two-component systems are studied in more detail than n-component systems. As a special case, we consider Hamiltonian and semi-Hamiltonian systems of Tsarëv.http://dx.doi.org/10.1155/S0161171204206147 |
| spellingShingle | M. B. Sheftel Symmetry group analysis and invariant solutions of hydrodynamic-type systems International Journal of Mathematics and Mathematical Sciences |
| title | Symmetry group analysis and invariant solutions of hydrodynamic-type systems |
| title_full | Symmetry group analysis and invariant solutions of hydrodynamic-type systems |
| title_fullStr | Symmetry group analysis and invariant solutions of hydrodynamic-type systems |
| title_full_unstemmed | Symmetry group analysis and invariant solutions of hydrodynamic-type systems |
| title_short | Symmetry group analysis and invariant solutions of hydrodynamic-type systems |
| title_sort | symmetry group analysis and invariant solutions of hydrodynamic type systems |
| url | http://dx.doi.org/10.1155/S0161171204206147 |
| work_keys_str_mv | AT mbsheftel symmetrygroupanalysisandinvariantsolutionsofhydrodynamictypesystems |