20,821 research outputs found
Three-dimensional structures of the spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials
The spatiotemporal nonlinear Schrödinger equation with power-law nonlinearity in PT-symmetric potentials is investigated, and two families of analytical three-dimensional spatiotemporal structure solutions are obtained. The stability of these solutions is tested by the linear stability analysis and the direct numerical simulation. Results indicate that solutions are stable below some thresholds for the imaginary part of PT-symmetric potentials in the self-focusing medium, while they are always unstable for all parameters in the self-defocusing medium. Moreover, some dynamical properties of these solutions are discussed, such as the phase switch, power and transverse power-flow density. The span of phase switch gradually enlarges with the decrease of the competing parameter k in PT-symmetric potentials. The power and power-flow density are all positive, which implies that the power flow and exchange from the gain toward the loss domains in the PT cell.Funded by the National Natural Science Foundation of China (Grant No. 11375007), the Zhejiang Provincial Natural Science Foundation of China (Grant
No. LY13F050006)
A perturbative approach to a class of Fokker-Planck equations
In this paper we present a direct perturbative method to solving certain
Fokker-Planck equations, which have constant diffusion coefficients and some
small parameters in the drift coefficients. The method makes use of the
connection between the Fokker-Planck and Schr\"odinger equations. Two examples
are used to illustrate the method. In the first example the drift coefficient
depends only on time but not on space. In the second example we consider the
Uhlenbeck-Ornstein process with a small drift coefficient. These examples show
that the such perturbative approach can be a useful tool to obtain approximate
solutions of Fokker-Planck equations with constant diffusion coefficients.Comment: 5 pages, no figure
Development and construction of China
Libraries in China's higher education institutions have been developing in keeping pace with the flourishing development of China's higher education. This article aims to make an introduction to the construction of China's higher education libraries, especially the recent three decades' achievements since China's reform and opening-up in 1978. In this article, the authors draw a general picture of the development of libraries in China's higher education institutions, covering such eight aspects as management, types and positioning, organizational structure and personnel, expenditure and buildings, reader service, building and sharing of resources as well as automation system.</p
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