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This paper introduces a wavepacket-transform-based Gaussian beam method for solving the Schrödinger equation. We focus on addressing two computational issues of the Gaussian beam method: how to g...
We consider solutions of the Schrödinger equation with a weak time-dependent random potential. It is shown that when the two-point correlation function of the potential is rapidly decaying, then ...
A new approach called the Schr\"odinger Collective Intrinsic Model (SCIM) has been developed to achieve a microscopic description of the coupling between collective and intrinsic excitations.
Using the Gabor frame, we get some time-global dispersive estimates for the Schr¨odinger semi-group in anisotropic Lebesgue spaces, which include a time-global maximal function estimate in the space L...
The effective mass one-dimensional Schr¨odinger equation for the generalized Morse potential is solved by using Nikiforov-Uvarov method. Energy eigenvalues and corresponding eigenfunctions are comput...
We propose a family of reliable symplectic integrators adapted to the Discrete Non–Linear Schr¨odinger equation; based on an idea of Yoshida [12] we can construct high order numerical schemes, that re...
We discuss a class of normal forms of the completely resonant non–linear Schr¨odinger equation on a torus. We stress the geometric and combinatorial constructions arising from this study. Further anal...
We propose a family of reliable symplectic integrators adapted to the Discrete Non–Linear Schr¨odinger equation; based on an idea of Yoshida [12]we can construct high order numerical schemes, that res...
We consider the focusing (attractive) nonlinear Schr¨odinger (NLS) equation with an external, symmetric potential which vanishes at infinity and supports a linear bound state. We prove that the symm...
We consider the nonlinear Schr\"{o}dinger equation $(-\Delta +V(x))u = \Gamma(x) |u|^{p-1}u$, $x\in \R^n$ with $V(x) = V_1(x) \chi_{\{x_1>0\}}(x)+V_2(x) \chi_{\{x_1<0\}}(x)$ and $\Gamma(x) = \Gamma_1(...
We investigate the integrability of generalized nonautonomous nonlinear Schr\"odinger (NLS) equations governing the dynamics of the single- and double-component Bose-Einstein condensates (BECs). The ...
Let X be a Riemannian symmetric space of the noncompact type. We prove that the solution of the time-dependent Schr\"odinger equation on X with square integrable initial condition f is identically ze...
The plane wave stability properties of the conservative schemes of Besse and Fei et al. for the cubic Schr\"{o}dinger equation are analysed. Although the two methods possess many of the same conserva...
In this work, we generalize previous results about the Fractionary Schr\"{o}dinger Equation within the formalism of the theory of Tempered Ultradistributions. Several examples of the use of this theo...
Using a recently developed technique to solve Schr\"odinger equation for constant mass, we studied the regime in which mass varies with position i.e position dependent mass Schr\"odinger equation(PDMS...

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