Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy
In the paper, we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures, and conserved quantities. We give a Lax triad to construct a master symmetry and a hierarchy of non-isospectral disper...
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| Veröffentlicht in: | Journal of mathematical physics 2014-08, Vol.55 (8), p.1 |
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| creator | Fu, Wei Ilangovane, R. Tamizhmani, K. M. Zhang, Da-jun |
| description | In the paper, we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures, and conserved quantities. We give a Lax triad to construct a master symmetry and a hierarchy of non-isospectral dispersionless Kadomtsev-Petviashvili flows. These non-isospectral flows, together with the known isospectral dispersionless Kadomtsev-Petviashvili flows, form a Lie algebra, which is used to derive two sets of symmetries for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy. By means of the master symmetry, symmetries, Noether operator, and conserved covariants, Hamiltonian structures are constructed for both isospectral and non-isospectral dispersionless Kadomtsev-Petviashvili hierarchies. Finally, two sets of conserved quantities and their Lie algebra are derived for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy. |
| doi_str_mv | 10.1063/1.4890480 |
| format | Article |
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M. ; Zhang, Da-jun</creator><creatorcontrib>Fu, Wei ; Ilangovane, R. ; Tamizhmani, K. M. ; Zhang, Da-jun</creatorcontrib><description>In the paper, we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures, and conserved quantities. We give a Lax triad to construct a master symmetry and a hierarchy of non-isospectral dispersionless Kadomtsev-Petviashvili flows. These non-isospectral flows, together with the known isospectral dispersionless Kadomtsev-Petviashvili flows, form a Lie algebra, which is used to derive two sets of symmetries for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy. By means of the master symmetry, symmetries, Noether operator, and conserved covariants, Hamiltonian structures are constructed for both isospectral and non-isospectral dispersionless Kadomtsev-Petviashvili hierarchies. 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M.</creatorcontrib><creatorcontrib>Zhang, Da-jun</creatorcontrib><title>Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy</title><title>Journal of mathematical physics</title><description>In the paper, we investigate integrability characteristics for the dispersionless Kadomtsev-Petviashvili hierarchy. These characteristics include symmetries, Hamiltonian structures, and conserved quantities. We give a Lax triad to construct a master symmetry and a hierarchy of non-isospectral dispersionless Kadomtsev-Petviashvili flows. These non-isospectral flows, together with the known isospectral dispersionless Kadomtsev-Petviashvili flows, form a Lie algebra, which is used to derive two sets of symmetries for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy. By means of the master symmetry, symmetries, Noether operator, and conserved covariants, Hamiltonian structures are constructed for both isospectral and non-isospectral dispersionless Kadomtsev-Petviashvili hierarchies. Finally, two sets of conserved quantities and their Lie algebra are derived for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy.</description><subject>Algebra</subject><subject>Construction</subject><subject>Dispersion</subject><subject>Hierarchies</subject><subject>Lie groups</subject><subject>Mathematics</subject><subject>Physics</subject><subject>Quantum theory</subject><subject>Symmetry</subject><issn>0022-2488</issn><issn>1089-7658</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2014</creationdate><recordtype>article</recordtype><recordid>eNp9kE1LAzEQhoMoWKsH_8GCJw9bJx-bTY5StBYL9aDnMJtN3JS2W5O00H_vSnv2NDA87zvDQ8g9hQkFyZ_oRCgNQsEFGVFQuqxlpS7JCICxkgmlrslNSisASpUQI7Kcb7P7jtiEdcjHYhf7nYs5uFT0vsidK9qQhk0K_XbtUirese03OblD-eHyIWDqDkOy6IKLGG13vCVXHtfJ3Z3nmHy9vnxO38rFcjafPi9KyxnkssFKovfQgKhaoSzWnjctk1gjSuS6ttxzjwLqxtu20mgtInoh0VnKGsnH5OHUO3z8s3cpm1W_j9vhpGGUyarWoP-laCWB10wzPVCPJ8rGPqXovNnFsMF4NBTMn1VDzdkq_wWuJGtX</recordid><startdate>20140801</startdate><enddate>20140801</enddate><creator>Fu, Wei</creator><creator>Ilangovane, R.</creator><creator>Tamizhmani, K. 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By means of the master symmetry, symmetries, Noether operator, and conserved covariants, Hamiltonian structures are constructed for both isospectral and non-isospectral dispersionless Kadomtsev-Petviashvili hierarchies. Finally, two sets of conserved quantities and their Lie algebra are derived for the isospectral dispersionless Kadomtsev-Petviashvili hierarchy.</abstract><cop>New York</cop><pub>American Institute of Physics</pub><doi>10.1063/1.4890480</doi><oa>free_for_read</oa></addata></record> |
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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Algebra Construction Dispersion Hierarchies Lie groups Mathematics Physics Quantum theory Symmetry |
| title | Integrability properties of the dispersionless Kadomtsev-Petviashvili hierarchy |
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