We derive a dispersion estimate for one-dimensional perturbed radial Schrödinger operators. We also derive several new estimates for solutions of the underlying differential equation and investigate the behavior of the Jost function near the edge of the continuous spectrum.

The direct and inverse scattering problems are analyzed for a first-order discrete system associated with the semi-discrete version of derivative NLS system. Jost solutions, coefficients, bound-state dependency norming constants investigated related to corresponding quantities two particular linear systems data set any multiplicities is described in an elegant manner terms pair constant matrix ...

The principal results of this paper consist of an intrinsic definition of the Evans function in terms of newly introduced generalized matrix-valued Jost solutions for general first-order matrix-valued differential equations on the real line, and a proof of the fact that the Evans function, a finite-dimensional determinant by construction, coincides with a modified Fredholm determinant associate...

A. Türler, Ch.E. Düllmann, H.W. Gäggeler, S. Soverna (Univ. Bern & PSI), R. Dressler, B. Eichler, F. Glaus, D.T. Jost, D. Piguet (PSI), T.N. Ginter, K.E. Gregorich, U. Kirbach, D.M. Lee, R. Sudowe, (LBNL), D.C. Hoffman, H. Nitsche, J.B. Patin, P. Zielinski (UC Berkeley & LBNL), W. Brüchle, R. Eichler, E. Jäger, V. Pershina, M. Schädel, B. Schausten, E. Schimpf, H.-J. Schött, G. Wirth (GSI), S.N...