A propagation method for time-dependent Schrodinger equations with an explicitly time-dependent Hamiltonian is developed where time ordering is achieved iteratively. The explicit time dependence of the time-dependent Schrodinger equation is rewritten as an inhomogeneous term. At each step of the iteration, the resulting inhomogeneous Schrodinger equation is solved with the Chebychev propagation...

A coherent atomic beam splitter can be realized using the transient dynamics of a chaotic system. We have experimentally observed such an effect using ultracold rubidium atoms. Our experimental results are in good agreement with numerical simulations of the Schrodinger equation for the system.

The harmonic oscillator in anti de Sitter space(AdS) is discussed. We consider the harmonic oscillator potential and then time independent Schrodinger equation in AdS space. Then we apply the supersymmetric Quantum Mechanics approach to solve our differential equation. In this paper we have solved Schrodinger equation for harmonic oscillator in AdS spacetime by supersymmetry approach. The shape...

Intermediate-depth, Boussinesq-type modelling is used to generalize previously known results for surface water waves propagating over arbitrarily shaped topographies. The improved reduced wave model is obtained after studying how small changes in the linear dispersion relation (over a flat bottom) can become dramatically important in the presence of a highly fluctuating topography. Numerical va...

This paper describes a σ -coordinate scalar transport model coupled with a Boussinesq-type hydrodynamic model. The Boussinesq model has the ability to calculate both three-dimensional velocity distributions and the water surface motion. To capture ‘dispersion’ processes in open channel flow, horizontal vorticity effects induced by a bottom shear stress are included in the Boussinesq model. Thus...

The global Galerkin method is applied to the benchmark problem that considers an oscillatory regime of convection of air in a tall two-dimensional rectangular cavity. The three most unstable modes of the linearized system of the Boussinesq equations are studied. The converged values of the critical Rayleigh numbers together with the corresponding oscillation frequencies are calculated for each ...

(Received July 23, 2013; in nal form February 26, 2014) In this paper, the (G′/G, 1/G) and (1/G′)-expansion methods with the aid of Maple are used to obtain new exact traveling wave solutions of the Boussinesq equation and the system of variant Boussinesq equations. The travelling wave solutions are expressed by the hyperbolic functions, the trigonometric functions, and the rational functions. ...

The accurate numerical simulation of wave disturbance within harbours requires consideration of both nonlinear and dispersive wave processes in order to capture such physical effects as wave refraction and diffraction, and nonlinear wave interactions such as the generation of harmonic waves. The Boussinesq equations are the simplest class of mathematical model that contain all these effects in ...

where p = p(x, t) is the scalar pressure, u = u(x, t) is the velocity vector field, and θ = θ (x, t) is a scalar quantity such as the concentration of a chemical substance or the temperature variation in a gravity field, in which case θe represents the buoyancy force. The nonnegative parameters μ and ν denote the molecular diffusion and the viscosity, respectively; u · ∇u := ua∂au, ∂au := ∂u ∂...