Browsing by Author "Aktosun, Tuncay"
Now showing 1 - 20 of 33
- Results Per Page
- Sort Options
Item Asymptotics of the scattering coefficients for a generalized Schrodinger equation(1998-04) Aktosun, Tuncay; Klaus, MartinItem The Borg-Marchenko theorem with a continuous spectrum(2005-10) Aktosun, Tuncay; Weder, RicardoItem Construction of the half-line potential from the Jost function(2003-05) Aktosun, TuncayFor the one-dimensional Schrödinger equation, the analysis is provided to recover the portion of the potential lying to the right (left) of any chosen point. The scattering data used consists of the left (right) Jost solution or its spatial derivative evaluated at that point, or the amplitudes of such functions. Various uniqueness and nonuniqueness results are established, and the recovery is illustrated with some explicit examples.Item Darboux transformation for the schrödinger equation with steplike potentials(1999-10) Aktosun, TuncayItem Direct and inverse scattering for selfadjoint Hamiltonian systems on the line(1999-02) Aktosun, Tuncay; Klaus, Martin; van der Mee, CornelisItem Exact solutions to the focusing nonlinear Schrödinger equation(2007-02) Aktosun, Tuncay; Demontis, Francesco; van der Mee, CornelisItem Explicit solutions to the Korteweg-de Vries equation on the half line(2006-05) Aktosun, Tuncay; van der Mee, CornelisItem Factorization and small-energy asymptotics for the radial schrödinger equation(1999-12) Aktosun, TuncayItem Factorization of scattering matrices due to partitioning of potentials in one-dimensional Schrodinger-type equations(1996-05) Aktosun, Tuncay; Klaus, Martin; van der Mee, CornelisItem Integral equation methods for the inverse problem with discontinuous wavespeed(1996-01) Aktosun, Tuncay; Klaus, Martin; van der Mee, CornelisItem Inverse Problem on the Line without Phase Information(1997-10) Aktosun, Tuncay; Sacks, Paul E.Item Inverse scattering for vowel articulation with frequency-domain data(2004-10) Aktosun, TuncayItem Inverse Scattering in One-Dimensional Nonconservative Media(1997-06) Aktosun, Tuncay; Klaus, Martin; van der Mee, CornelisItem Inverse scattering on the line for a generalized nonlinear Schrödinger equation(2004-01) Aktosun, Tuncay; Papanicolaou, Vassilis G.; Zisis, VassilisItem Inverse scattering on the line with incomplete scattering data(2003-12) Aktosun, TuncayItem Inverse scattering to determine the shape of a vocal tract(2005-03) Aktosun, TuncayItem Inverse scattering transform, KdV, and solitons(2003-05) Aktosun, TuncayIn this review paper, the Korteweg-de Vries equation (KdV) is considered, and it is derived by using the Lax method and the AKNS method. An outline of the inverse scattering problem and of its solution is presented for the associated Schrödinger equation on the line. The inverse scattering transform is described to solve the initial-value problem for the KdV, and the time evolution of the corresponding scattering data is obtained. Soliton solutions to the KdV are derived in several ways.Item Inverse scattering with partial information on the potential(2001-02) Aktosun, Tuncay; Weder, RicardoThe one-dimensional Schröddinger equation is considered when the potential is real valued and integrable and has a finite first moment. The recovery of such a potential is analyzed in terms of the scattering data consisting of a reflection coefficient, all the bound-state energies, knowledge of the potential on a finite interval, and all of the bound-state norming constants except one. It is shown that a missing norming constant in the data can cause at most a double nonuniqueness in the recovery. In the particular case when the missing norming constant in the data corresponds to the lowest-energy bound state, the necessary and sufficient conditions are obtained for the nonuniqueness, and the two norming constants and the corresponding potentials are determined. Some explicit examples are provided to illustrate the nonuniqueness.Item Inverse Schrodinger scattering on the line with partial knowledge of the potential(1995-08) Aktosun, TuncayItem Inverse spectral-scattering problem with two sets of discrete spectra for the radial Schrödinger equation(2004-02) Aktosun, Tuncay; Weder, Ricardo