Browsing Faculty Works, Department of Mathematics by Subject "line"
Now showing items 18 of 8

asymptotics of the scattering coefficients for a generalized Schrodinger equation
(AIP Publishing, 199908)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 ... 
continuity of the Smatrix for the perturbed Hill's equation
(AIP Publishing, 199407)The behavior of the scattering matrix associated with the perturbed Hill's equation as the spectral parameter approaches an endpoint of a spectral band is studied. In particular, the continuity of the scattering matrix at ... 
inverse wave scattering with discontinuous wave speed
(AIP Publishing, 199506)The inverse scattering problem on the line is studied for the generalized Schrödinger equation (d 2ψ/dx 2)+k 2 H(x)2ψ=Q(x)ψ, where H(x) is a positive, piecewise continuous function with positive limits H ± as x → ±∞. This ... 
on the number of bound states for the onedimensional Schrodinger equation
(AIP Publishing, 199809)The number of bound states of the onedimensional 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 RiemannHilbert problem for the onedimensional Schrodingerequation
(AIP Publishing, 199307)A matrix RiemannHilbert problem associated with the onedimensional Schrodinger equation is considered, and the existence and uniqueness of its solutions are studied. The solution of this RiemannHilbert problem yields ... 
scattering and inverse scattering in onedimensional nonhomogeneous media
(AIP Publishing, 199205)The wave propagation in a onedimensional nonhomogeneous medium is considered, where the wave speed and the restoring force depend on location. In the frequency domain this is equivalent to the Schrodinger equation d2psi/dx2 ... 
wave operators for the matrix ZakharovShabat system
(AIP Publishing, 201005)In this article, we prove the similarity (and, in the focusing case, the Junitary 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, 199804)Wave scattering is analyzed in a onedimensional 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 ...