Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy
| dc.contributor.author | Liu, Q. P. | |
| dc.contributor.author | Mañas Baena, Manuel Enrique | |
| dc.date.accessioned | 2023-06-20T20:09:10Z | |
| dc.date.available | 2023-06-20T20:09:10Z | |
| dc.date.issued | 1999-03 | |
| dc.description | ©Springer. | |
| dc.description.abstract | We consider the vectorial approach to the binary Darboux transformations for the Kadomtsev-Petviashvili hierarchy in its Zakharov-Shabat formulation. We obtain explicit formulae for the Darboux transformed potentials in terms of Grammian type determinants. We also study the n-th Gel'fand-Dickey hierarchy introducing spectral operators and obtaining similar results. We reduce the above-mentioned results to the Kadomtsev-Petviashvili I and II real forms, obtaining corresponding vectorial Darboux transformations. In particular for the Kadomtsev-Petviashvili I hierarchy, we get the line soliton, the lump solution, and the Johnson-Thompson lump, and the corresponding determinant formulae for the nonlinear superposition of several of them. For Kadomtsev-Petviashvili II apart from the line solitons, we get singular rational solutions with its singularity set describing the motion of strings in the plane. We also consider the I and II real forms for the Gel'fand-Dickey hierarchies obtaining the vectorial Darboux transformation in both cases. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/32483 | |
| dc.identifier.doi | 10.1007/s003329900070 | |
| dc.identifier.issn | 0938-8974 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1007/s003329900070 | |
| dc.identifier.relatedurl | http://link.springer.com | |
| dc.identifier.relatedurl | http://arxiv.org/abs/solv-int/9705012 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/59691 | |
| dc.issue.number | 2 | |
| dc.journal.title | Journal of nonlinear science | |
| dc.language.iso | eng | |
| dc.page.final | 232 | |
| dc.page.initial | 213 | |
| dc.publisher | Springer | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Time-dependent schrodinger | |
| dc.subject.keyword | Inverse scattering transform | |
| dc.subject.keyword | Rational solutions | |
| dc.subject.keyword | Davey-stewartson | |
| dc.subject.keyword | Gauge transformations | |
| dc.subject.keyword | Jacobian varieties | |
| dc.subject.keyword | Soliton-equations | |
| dc.subject.keyword | Kp hierarchy | |
| dc.subject.keyword | Evolution | |
| dc.subject.keyword | Systems | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Vectorial Darboux transformations for the Kadomtsev-Petviashvili hierarchy | |
| dc.type | journal article | |
| dc.volume.number | 9 | |
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| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication.latestForDiscovery | 0d5b5872-7553-4b33-b0e5-085ced5d8f42 |
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