Wave operators for the matrix Zakharov-Shabat system
| dc.contributor | Virginia Tech | en |
| dc.contributor.author | Klaus, Martin | en |
| dc.contributor.author | van der Mee, Cornelis | en |
| dc.contributor.department | Mathematics | en |
| dc.date.accessed | 2014-03-20 | en |
| dc.date.accessioned | 2014-04-09T18:12:29Z | en |
| dc.date.available | 2014-04-09T18:12:29Z | en |
| dc.date.issued | 2010-05 | en |
| dc.description.abstract | In this article, we prove the similarity (and, in the focusing case, the J-unitary equivalence) of the free Hamiltonian and the restriction of the full Hamiltonian to the maximal invariant subspace on which its spectrum is real for the matrix Zakharov-Shabat system under suitable conditions on the potentials. This restriction of the full Hamiltonian is shown to be a scalar-type spectral operator whose resolution of the identity is evaluated. In the focusing case, the restricted full Hamiltonian is an absolutely continuous, J-self-adjoint non-J-definitizable, operator allowing a spectral theorem without singular critical points. To illustrate the results, two examples are provided. (C) 2010 American Institute of Physics. [doi:10.1063/1.3377048] | en |
| dc.description.sponsorship | Italian Ministry of University Education and Research (MIUR) 20083KLJJEZ | en |
| dc.description.sponsorship | Autonomous Region of Sardinia | en |
| dc.identifier.citation | Klaus, M.; van der Mee, C., "Wave operators for the matrix Zakharov-Shabat system," J. Math. Phys. 51, 053503 (2010); http://dx.doi.org/10.1063/1.3377048 | en |
| dc.identifier.doi | https://doi.org/10.1063/1.3377048 | en |
| dc.identifier.issn | 0022-2488 | en |
| dc.identifier.uri | http://hdl.handle.net/10919/47098 | en |
| dc.identifier.url | http://scitation.aip.org/content/aip/journal/jmp/51/5/10.1063/1.3377048 | en |
| dc.language.iso | en_US | en |
| dc.publisher | AIP Publishing | en |
| dc.rights | In Copyright | en |
| dc.rights.uri | http://rightsstatements.org/vocab/InC/1.0/ | en |
| dc.subject | inverse scattering | en |
| dc.subject | hamiltonian-systems | en |
| dc.subject | eigenvalues | en |
| dc.subject | line | en |
| dc.title | Wave operators for the matrix Zakharov-Shabat system | en |
| dc.title.serial | Journal of Mathematical Physics | en |
| dc.type | Article - Refereed | en |
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