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EnglishIn 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.
Wave operators for the matrix Zakharov-Shabat system / MARTIN KLAUS; VAN DER MEE C. - 51(2010), pp. 053503-053528.
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| Titolo: | Wave operators for the matrix Zakharov-Shabat system |
| Autori: | |
| Data di pubblicazione: | 2010 |
| Rivista: | |
| Citazione: | Wave operators for the matrix Zakharov-Shabat system / MARTIN KLAUS; VAN DER MEE C. - 51(2010), pp. 053503-053528. |
| 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. |
| Handle: | http://hdl.handle.net/11584/21938 |
| Tipologia: | 1.1 Articolo in rivista |
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