912 research outputs found
Transverse Patterns in Nonlinear Optical Resonators
The book is devoted to the formation and dynamics of localized structures
(vortices, solitons) and extended patterns (stripes, hexagons, tilted waves) in
nonlinear optical resonators such as lasers, optical parametric oscillators,
and photorefractive oscillators. The theoretical analysis is performed by
deriving order parameter equations, and also through numerical integration of
microscopic models of the systems under investigation. Experimental
observations, and possible technological implementations of transverse optical
patterns are also discussed. A comparison with patterns found in other
nonlinear systems, i.e. chemical, biological, and hydrodynamical systems, is
given. This article contains the table of contents and the introductory chapter
of the book.Comment: 37 pages, 14 figures. Table of contents and introductory chapter of
the boo
Ultrasonic cavity solitons
We report on a new type of localized structure, an ultrasonic cavity soliton,
supported by large aspect-ratio acoustic resonators containing viscous media.
The spatio-temporal dynamics of this system is analyzed on the basis of a
generalized Swift-Hohenberg equation, derived from the microscopic equations
under conditions close to nascent bistability. These states of the acoustic and
thermal fields are robust structures, existing whenever a spatially uniform
solution and a periodic pattern coexist. An analytical solution for the
ultrasonic cavity soliton is also presented
Self collimation of ultrasound in a 3D sonic crystal
We present the experimental demonstration of self-collimation (subdiffractive
propagation) of an ultrasonic beam inside a three-dimensional sonic crystal.
The crystal is formed by two crossed steel cylinders structures in a
woodpile-like geometry disposed in water. Measurements of the 3D field
distribution show that a narrow beam which diffractively spreads in the absence
of the sonic crystal is strongly collimated in propagation inside the crystal,
demonstrating the 3D self-collimation effect.Comment: 3 figures, submitted to Applied Physics Letter
Exact soliton solutions of the one-dimensional complex Swift-Hohenberg equation
Using Painlev\'e analysis, the Hirota multi-linear method and a direct ansatz
technique, we study analytic solutions of the (1+1)-dimensional complex cubic
and quintic Swift-Hohenberg equations. We consider both standard and
generalized versions of these equations. We have found that a number of exact
solutions exist to each of these equations, provided that the coefficients are
constrained by certain relations. The set of solutions include particular types
of solitary wave solutions, hole (dark soliton) solutions and periodic
solutions in terms of elliptic Jacobi functions and the Weierstrass
function. Although these solutions represent only a small subset of the large
variety of possible solutions admitted by the complex cubic and quintic
Swift-Hohenberg equations, those presented here are the first examples of exact
analytic solutions found thus far.Comment: 32 pages, no figures, elsart.cl
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