We prove global-in-time Strichartz-type estimates for the Schr\"{o}dinger equation on manifolds of form $\mathbb{R}^{n}\times \mathbb{T}^{d}$, where $\mathbb{T}^{d}$ is a $d$-dimensional torus. Our results generalize and improve global space-time estimate $\mathbb{R} \times \mathbb{T}^{2}$ due to Z. Hani B. Pausader.

This article consists of Improved Bernoulli Sub-Equation Function Method (IBSEFM) to get the new solutions nonlinear fractional Schrödinger equation described by beta-derivative. Foremost, it is dealt with derivative Atangana. Secondly, basic properties IBSEFM are given. Finally, proposed method has been applicated considered its solutions. Moreover, graphs obtained plotted via Mathematica. It ...

In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrödinger equation. Then, in the case of separated variables, by requiring that the conjugate momentum be invariant under any linear transformation of the solutions of the Schrödinger equation used in the reduced action, we clearly identify...

We prove unique continuation principles for solutions of evolution Schrödinger equations with time dependent potentials. These correspond to uncertainly principles of Paley-Wiener type for the Fourier transform. Our results extends to a large class of semi-linear Schrödinger equation. Titre : Un théoreme de type Paley-Wiener pour les évolutions de Schrodinger. Résumé : On prouve des principes d...

In this paper, a trial function method is employed to find exact solutions the nonlinear Schrödinger equations with high-order time-dependent coefficients. This system might be used describe propagation of ultrashort optical pulses in fibers, self-steepening and self-frequency shift effects. The new general are found for case <mro...