Tuncay Aktosun

TL;DR: In this paper, the authors considered the recovery of a spherically-symmetric wave speed from the set of the corresponding transmission eigenvalues for which the corresponding eigenfunctions are also symmetric and showed that the unique recovery is obtained when the data contains one additional piece of information.

TL;DR: In this article, the authors considered the recovery of a spherically symmetric wave speed v from the set of corresponding transmission eigenvalues for which the corresponding eigenfunctions are also symmetric, assuming that there exists at least one v corresponding to the data.

TL;DR: In this paper, a method is given to construct globally analytic (in space and time) exact solutions to the focusing cubic nonlinear Schrodinger equation on the line, which can alternatively be written explicitly as algebraic combinations of exponential, trigonometric and polynomial functions of the spatial and temporal coordinates.

TL;DR: In this paper, the Schrodinger equation on the half-line is considered with a real-valued, integrable potential having a finite first moment, and it is shown that the potential and the boundary conditions are uniquely determined by the data containing the discrete eigenvalues for a boundary condition at the origin, the continuous part of the spectral measure for that boundary condition and a subset of the discrete values for a different boundary condition.

TL;DR: In this paper, a systematic method is presented to provide various equivalent solution formulas for exact solutions to the sine-Gordon equation, where the inverse scattering transform is applied via the use of a Marchenko integral equation.