Virginia TechAktosun, T.Klaus, Martin2014-04-092014-04-091999-08Aktosun, T.; Klaus, M., "Asymptotics of the scattering coefficients for a generalized Schrödinger equation," J. Math. Phys. 40, 3701 (1999); http://dx.doi.org/10.1063/1.5329200022-2488http://hdl.handle.net/10919/47025The 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 scattering coefficients near zeros of F is analyzed. It is shown that in the so-called exceptional case, the values of the scattering coefficients at a zero of F may be affected by P(x). The location of the k-values in the complex plane where the exceptional case can occur is studied. Some examples are provided to illustrate the theory. (C) 1999 American Institute of Physics. [S0022-2488(99)03007-8].en-USIn Copyrightriemann-hilbert probleminverse scatteringwave scatteringenergylineAsymptotics of the scattering coefficients for a generalized Schrödinger equationArticle - Refereedhttp://scitation.aip.org/content/aip/journal/jmp/40/8/10.1063/1.532920Journal of Mathematical Physicshttps://doi.org/10.1063/1.532920