Virginia TechKlaus, Martinvan der Mee, Cornelis2014-04-092014-04-092010-05Klaus, M.; van der Mee, C., "Wave operators for the matrix Zakharov-Shabat system," J. Math. Phys. 51, 053503 (2010); http://dx.doi.org/10.1063/1.33770480022-2488http://hdl.handle.net/10919/47098In 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-USIn Copyrightinverse scatteringhamiltonian-systemseigenvalueslineArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/51/5/10.1063/1.3377048https://doi.org/10.1063/1.3377048