This book introduces graduate students and researchers in mathematics and the sciences to
the multifaceted subject of the equations of hyperbolic type, which are used, in particular, to …

Abstract Modeling in Nonlinear Optics, and also in other fields of Physics and Mechanics,
yields interesting and difficult problems due to the presence of several different scales of …

This paper studies high frequency solutions of nonlinear hyperbolic equations for time
scales at which diffractive effects and nonlinear effects are both present in the leading term …

Many results have been obtained in the last decade about the justification of nonlinear
geometric optics expansions (see references below and the survey papers [JMR1][JMR2]) …

Oscillating approximate solutions to nonlinear hyperbolic dispersive systems are studied.
Ansatz of three scales are used in order to deal with diffractive effects. The scaling of the …

This paper considers the behavior of pulse-like solutions of length ε≪1 to semilinear
systems of hyperbolic partial differential equations on the time scale t=O(1/\eps) of diffractive …

In this paper, we derive rigorously the nonlinear Schrödinger equation and Davey–
Stewartson systems from quadratic hyperbolic systems using nonlinear diffractive geometric …

We derive various approximations for the solutions of nonlinear hyperbolic systems with
fastly oscillating initial data. We first provide error estimates for the so-called slowly varying …

We study, for times of order 1/ε, solutions of wave equations which are O (ε^ 2) modulations
of an ε periodic wave equation. The solutions are of slowly varying amplitude type built on …

This paper studies highly oscillatory solutions to a class of systems of semilinear hyperbolic
equations with a small parameter, in a setting that includes Klein–Gordon equations and the …