In this paper, we consider the nonlinear Schrödinger equation ut + i∆u − F (u) = 0 in two dimensions. We show, by an operator-theoretic proof, that the well-known Lie and Strang formulae (which are splitting methods) are approximations of the exact solution of order 1 and 2 in time.
The stability of five finite difference–time domain (FD–TD) schemes coupling Maxwell equations to Debye or Lorentz models has been analyzed in [P. Petropoulos, Stability and phase error analysis of FD–TD in dispersive dielectrics, IEEE Trans. where numerical evidence for specific media have been used. We use von Neumann analysis to give necessary and… (More)
We investigate the dynamics of a chain of oscillators coupled by fully-nonlinear interaction potentials. This class of models includes Newton's cradle with Hertzian contact interactions between neighbors. By means of multiple-scale analysis, we give a rigorous asymptotic description of small amplitude solutions over large times. The envelope equation… (More)
This article describes a new kind of processing chain based on a non-uniform sampling scheme provided by a level-crossing ADC. The chain implements IIR filters which process directly the non-uniform samples without resampling in a regular scheme. The non-uniformity in the sample times leads to choose a state representation for the filters. The stability is… (More)