اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدPseudospectral Algorithms for Solving Nonlinear Schroedinger Equation in 3D
167
0
0.0
(
0
)
تأليف
A. A. Skorupski
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
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.
قيم البحث
اقرأ أيضاً
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
non-overlapping intervals whose size is chosen according to the local de Broglie wavelength. A multi-domain weak formulation of the Schrodinger equation is obtained by representing the wavefunction by Lagrange polynomials with compact support in each domain, discretized at the Legendre-Gauss-Lobatto points. The resulting Hamiltonian is sparse, allowing for efficient diagonalization and storage. Accurate time evolution is carried out by the Chebychev propagator, involving only sparse matrix-vector multiplications. Our approach combines the efficiency of mapped grid methods with the accuracy of spectral representations based on Gaussian quadrature rules and the stability and convergence properties of polynomial propagators. We apply this method to high-harmonic generation and examine the role of the initial state for the harmonic yield near the cutoff.
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
g nonlinearity to obtain results on existence, shape, stability and dynamics of the soliton. The main result of this paper (Theorem 1) shows that for {epsilon}to0 the orbit of our soliton approaches the orbit of a classical particle in a potential V(x).
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
able but the convergence to equilibrium occurs on astronomical time scales and becomes increasingly slower as a result of a coarsening processes. Stationary negative-temperature states can be experimentally generated via boundary dissipation or from free expansions of wave packets initially at positive temperature equilibrium.
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
ce of finite energy weak solutions, these results are then applied to the analysis of finite energy weak solutions for Quantum Magnetohydrodynamic systems.
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
to account. This modified equation cannot be reduced to the standard derivative nonlinear Schroedinger equation and hence its possible integrability and related properties need to be established afresh. Indeed, the new equation is shown to be integrable by the existence of a bi--Hamiltonian structure, which yields the recursion operator needed to generate an infinite sequence of conserved densities. Some of these have been found explicitly by symbolic computations based on the symmetry properties of the new equation. Since the new equation includes as a special case the derivative nonlinear Schroedinger equation, the recursion operator for the latter one is now readily available.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
