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#### wave operators for the matrix Zakharov-Shabat system

(AIP Publishing, 2010-05)

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 ...

#### wave scattering in one dimension with absorption

(AIP Publishing, 1998-04)

Wave scattering is analyzed in a one-dimensional nonconservative medium governed by the generalized Schrodinger equation d(2) psi/dx(2)+k(2) psi=[ikP(x)+Q(x)]psi, where P(x) and Q(x) are real, integrable potentials with ...

#### on the number of bound states for the one-dimensional Schrodinger equation

(AIP Publishing, 1998-09)

The number of bound states of the one-dimensional Schrodinger equation is analyzed in terms of the number of bound states corresponding to ''fragments'' of the potential. When the potential is integrable and has a finite ...

#### on the Riemann-Hilbert problem for the one-dimensional Schrodinger-equation

(AIP Publishing, 1993-07)

A matrix Riemann-Hilbert problem associated with the one-dimensional Schrodinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this Riemann-Hilbert problem yields ...

#### asymptotics of the scattering coefficients for a generalized Schrodinger equation

(AIP Publishing, 1999-08)

The generalized Schrodinger equation d(2)psi/dx(2) + F(k)psi=[ikP(x) + Q(x)]psi is considered, where P and Q are integrable potentials with finite first moments and F satisfies certain conditions. The behavior of the ...