It is well known that for certain parameter regimes the periodic focusing Non-linear Schrödinger (NLS) equation exhibits a chaotic response when the system is perturbed. When even symmetry is imposed the mechanism for chaotic behavior is due to the symmetric subspace being separated by...

The computation of incompressible turbulent flow with two-equation closure models (k-ε and k-ω) is considered. The Cartesian staggered grid approach is generalized to general boundary-fitted coordinates. An accurate discretization on nonsmooth grids is presented. For higher-order monotone...

A family of finite-difference methods is used to transform the initial/boundary-value problem associated with the nonlinear Schrödinger equation into a first-order, linear, initial-value problem. Numerical methods are developed by replacing the time and space derivatives by central-difference...

We consider the numerical solution of the AKNS eigenproblem associated with the nonlinear Schrödinger equation. Four finite difference methods are considered: two standard schemes (forward and central differences), a discretization introduced by Ablowitz and Ladik (1976), and a modified version...

The main properties of the focusing nonlinear Schrödinger equation for a multidimensional wavepacket envelop are reviewed. The coupling to a mean field or to low frequency acoustic waves stirred by the wavepacket is analyzed.

Computer simulations of dynamical systems contain discretizations, where finite machine arithmetic replaces continuum state space. For chaotic dynamical systems, the main features of this discretization are stochastically related to the parameters both, of the underlying continuous system and of...

Identification of the internal flow dynamics in catchments is difficult because of the lack of information in precipitation-stream discharge time series alone. Two experimental catchments, Hydrohill and Nandadish, near Nanjing in China, have been set up to monitor internal flows reaching the...

The theory of purchasing power parity (PPP) has worked poorly during the post-Bretton Woods period. We generalize the concept of PPP (called generalized-PPP, or G-PPP) and posit an equilibrium relationship among groups of real exchange rates. The basic tenants of G-PPP are that real fundamental...

This paper demonstrates two independent methodologies for the regional allocation of world greenhouse gas emission reductions; one based on mathematical programming and the other on a game theoretic method known as the Shapley value. Both methodologies make use of the solution of a world...