Integrability conditions for Boussinesq type systems
The symmetry approach to the classification of evolution integrable partial differential equations (see, for example (Mikhailov et al.,1991)) produces an infinite series of functions, defined in terms of the right hand side, that are conserved densities of any equation having infinitely many infinit...
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Elsevier
2024-12-01
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| Series: | Partial Differential Equations in Applied Mathematics |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2666818124003450 |
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| author | R. Hernández Heredero V. Sokolov |
| author_facet | R. Hernández Heredero V. Sokolov |
| author_sort | R. Hernández Heredero |
| collection | DOAJ |
| description | The symmetry approach to the classification of evolution integrable partial differential equations (see, for example (Mikhailov et al.,1991)) produces an infinite series of functions, defined in terms of the right hand side, that are conserved densities of any equation having infinitely many infinitesimal symmetries. For instance, the function ∂f∂ux has to be a conserved density of any integrable equation of the KdV type ut=uxxx+f(u,ux). This fact imposes very strong conditions on the form of the function f. In this paper we construct similar canonical densities for equations of the Boussinesq type. In order to do that, we write the equations as evolution systems and generalise the formal diagonalisation procedure proposed in Mikhailov et al. (1987) to these systems. |
| format | Article |
| id | doaj-art-ae7696b0d5664cf7a7e1e450fada221a |
| institution | Kabale University |
| issn | 2666-8181 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Partial Differential Equations in Applied Mathematics |
| spelling | doaj-art-ae7696b0d5664cf7a7e1e450fada221a2024-12-13T11:05:44ZengElsevierPartial Differential Equations in Applied Mathematics2666-81812024-12-0112100959Integrability conditions for Boussinesq type systemsR. Hernández Heredero0V. Sokolov1ETSIS de Telecomunicación, Universidad Politécnica de Madrid, Madrid, SpainHigher School of Modern Mathematics MIPT, Moscow, Russia; Corresponding author.The symmetry approach to the classification of evolution integrable partial differential equations (see, for example (Mikhailov et al.,1991)) produces an infinite series of functions, defined in terms of the right hand side, that are conserved densities of any equation having infinitely many infinitesimal symmetries. For instance, the function ∂f∂ux has to be a conserved density of any integrable equation of the KdV type ut=uxxx+f(u,ux). This fact imposes very strong conditions on the form of the function f. In this paper we construct similar canonical densities for equations of the Boussinesq type. In order to do that, we write the equations as evolution systems and generalise the formal diagonalisation procedure proposed in Mikhailov et al. (1987) to these systems.http://www.sciencedirect.com/science/article/pii/S2666818124003450Boussinesq type systemsIntegrability conditionsSymmetries |
| spellingShingle | R. Hernández Heredero V. Sokolov Integrability conditions for Boussinesq type systems Partial Differential Equations in Applied Mathematics Boussinesq type systems Integrability conditions Symmetries |
| title | Integrability conditions for Boussinesq type systems |
| title_full | Integrability conditions for Boussinesq type systems |
| title_fullStr | Integrability conditions for Boussinesq type systems |
| title_full_unstemmed | Integrability conditions for Boussinesq type systems |
| title_short | Integrability conditions for Boussinesq type systems |
| title_sort | integrability conditions for boussinesq type systems |
| topic | Boussinesq type systems Integrability conditions Symmetries |
| url | http://www.sciencedirect.com/science/article/pii/S2666818124003450 |
| work_keys_str_mv | AT rhernandezheredero integrabilityconditionsforboussinesqtypesystems AT vsokolov integrabilityconditionsforboussinesqtypesystems |