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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 ...
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(...
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 paper, we consider the Cauchy problem of Nonlinear Schr¨odinger equationiut + u = λ1|u|p1u + λ2|u|p2u, t ∈ R, x ∈ RN u(0, x) = ϕ(x), x ∈ RN,where N ≥ 3, 0 < p1 < p2 < 4 N−2 , λ1 ...
In this short letter we show that the one dimensional non linear Schr¨odinger equation(NLS)can be solved by a Hopf-Cole transformation which converts it to the Burgers equation in turbulence.
An approximate method is proposed to solve position dependent mass Schr¨odinger equation. The procedure suggested here leads to the solution of the PDM Schr¨odinger equation without transforming the ...
An approximate method is proposed to solve position dependent mass Schr¨odinger equation. The procedure suggested here leads to the solution of the PDM Schr¨odinger equation without transforming the ...

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