Wave propagation in weakly nonlinear dispersive systems

Slow Passage through Resonance for a Weakly Nonlinear Dispersive Wave

Long-wave and short-wave asymptotics in nonlinear dispersive systems.

In this paper we study the interplay between short- and long-space scales in the context of conservative dispersive systems. We consider model systems in (1+1) dimensions that admit both long- and short-wavelength solutions in the linear regime. A nonlinear analysis of these systems is constructed, making use of multiscale expansions. We show that the equations governing the lowest order involv...

Asymmetric wave propagation in nonlinear systems.

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schrödinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency a...

Weakly dispersive modal pulse propagation in the North Pacific Ocean.

The propagation of weakly dispersive modal pulses is investigated using data collected during the 2004 long-range ocean acoustic propagation experiment (LOAPEX). Weakly dispersive modal pulses are characterized by weak dispersion- and scattering-induced pulse broadening; such modal pulses experience minimal propagation-induced distortion and are thus well suited to communications applications. ...

Error-propagation in weakly nonlinear inverse problems

In applications of inversion methods to real data, nonlinear inverse problems are often simpli ed to more easily solvable linearized inverse problems. By doing so one introduces an error made by the linearization. Nonlinear inverse methods are more accurate because the methods that are used are more correct from a physical point of view. However, if data are used that have a statistical error, ...