On the Number of Bound States for the 1-d Schr Odinger Equation

A New High Order Closed Newton-Cotes Trigonometrically-fitted Formulae for the Numerical Solution of the Schrodinger Equation

In this paper, we investigate the connection between closed Newton-Cotes formulae, trigonometrically-fitted methods, symplectic integrators and efficient integration of the Schr¨odinger equation. The study of multistep symplectic integrators is very poor although in the last decades several one step symplectic integrators have been produced based on symplectic geometry (see the relevant lit...

On the Direct and Inverse Scattering for the Matrix Schr Odinger Equation on the Line

The one-dimensional matrix Schrr odinger equation is considered when the matrix potential is selfadjoint and satisses certain general restrictions. The small-energy asymptotics of the scattering solutions and scattering coeecients are derived. The continuity of the scattering coeecients is established. The unique solvability of the corresponding matrix Marchenko integral equations is proved. Sh...

On Bound States for Systems of Weakly Coupled Schr Odinger Equations in One Space Dimension

INVERSE SCHR ODINGER SCATTERING ON THE LINEWITH PARTIAL KNOWLEDGE OF THE POTENTIALTuncay

The one-dimensional Schrr odinger equation is considered when the potential and its rst moment are absolutely integrable. The potential is uniquely constructed in terms of the scattering data consisting of the reeection coeecient from the right (left) and the knowledge of the potential on the right (left) half line of the real axis. Hence, neither the bound state energies nor the bound state no...

A Modulation Method for Self-focusing in the Perturbed Critical Nonlinear Schr Odinger Equation

In this Letter we introduce a systematic perturbation method for analyzing the e ect of small perturbations on critical self focusing by reducing the perturbed critical nonlinear Schrodinger equation (PNLS) to a simpler system of modulation equations that do not depend on the transverse variables. The modulation equations can be further simpli ed, depending on whether PNLS is power conserving ...