Wave operators for defocusing matrix Zakharov-Shabat systems with potentials nonvanishing at infinity

DEMONTIS, FRANCESCO;VAN DER MEE, CORNELIS VICTOR MARIA

2010-01-01

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Abstract

In this article we prove that the wave operators describing the direct scattering of the defocusing matrix Zakharov-Shabat system with potentials having distinct nonzero values with the same modulus at ±∞ exist, are asymptotically complete, and lead to a unitary scattering operator. We also prove that the free Hamiltonian operator is absolutely continuous.