We investigate L1→L∞ dispersive estimates for the one dimensional Dirac equation with a potential. In particular, we show that evolution satisfies natural t−12 decay rate, which may be improved to t−32 at cost of spatial weights when thresholds are regular. classify structure threshold obstructions, showing there is most space each threshold. that, in presence resonance, and faster weighted bou...

This paper is devoted to the study of large-time asymptotics small solutions matrix nonlinear Schrödinger equation with a potential on half-line and general selfadjoint boundary condition, line point interaction, in whole supercritical regime. We prove that are scattering asymptotically time, t→±∞, behave as associated linear identically zero. The can be either generic or exceptional. Our appro...

In this paper, an inverse nodal problem for a second-order differential equation having a chemical potential on a finite interval is investigated. First, we estimate the nodal points and nodal lengths of differential operator. Then, we show that the potential can be uniquely determined by a dense set of nodes of the eigenfunctions.