We study the nonlinear wave equation utt ? c 2 uxx = (u) u(0; t) = 0 = u(; t) (0.1) with an analytic nonlinearity of the type (u) = u 3 + P k4 k u k. On each small{energy surface we consider a solution of the linearized system with initial datum having the proole of an elliptic sinus: we show that solutions starting close to the corresponding phase space trajectory remain close to it for times ...

Yearly electricity consumption trends of most developing countries usually exhibit approximately exponential growth curves. An optimized nonhomogeneous exponential model (ONEM) is proposed as a method of forecasting electricity consumption by using trend extrapolation. The parameters of the nonhomogeneous exponential equation are obtained by using the inverse accumulated generating operation, d...

The Bethe-Salpeter equation plays a crucial role in understanding the physics of correlated fermions, relating to optical excitations solids as well resonances high-energy physics. Yet, it is notoriously difficult control numerically, typically requiring an effort that scales polynomially with energy and accuracy. This puts many interesting systems out computational reach. Using intermediate re...