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Three pseudospectral algorithms are described (Euler, leapfrog and trapez) for solving numerically the time dependent nonlinear Schroedinger equation in one, two or three dimensions. Numerical stability regions in the parameter space are determined for the cubic nonlinearity, which can be easily extended to other nonlinearities. For the first two algorithms, maximal timesteps for stability are calculated in terms of the maximal Fourier harmonics admitted by the spectral method used to calculate space derivatives. The formulas are directly applicable if the discrete Fourier transform is used, i.e. for periodic boundary conditions. These formulas were used in the relevant numerical programs developed in our group.
We show that a pseudospectral representation of the wavefunction using multiple spatial domains of variable size yields a highly accurate, yet efficient method to solve the time-dependent Schrodinger equation. The overall spatial domain is split into
We study the behavior of the soliton solutions of the equation i((partial{psi})/(partialt))=-(1/(2m)){Delta}{psi}+(1/2)W_{{epsilon}}({psi})+V(x){psi} where W_{{epsilon}} is a suitable nonlinear term which is singular for {epsilon}=0. We use the stron
We explore the statistical behavior of the discrete nonlinear Schroedinger equation. We find a parameter region where the system evolves towards a state characterized by a finite density of breathers and a negative temperature. Such a state is metast
Motivated by some models arising in quantum plasma dynamics, in this paper we study the Maxwell-Schrodinger system with a power-type nonlinearity. We show the local well-posedness in $H^2(mathbb{R}^3)times H^{3/2}(mathbb{R}^3)$ and the global existen
Oblique propagation of magnetohydrodynamic waves in warm plasmas is described by a modified vector derivative nonlinear Schroedinger equation, if charge separation in Poissons equation and the displacement current in Amperes law are properly taken in