Dictionary Definition
breather
Noun
2 air passage provided by a retractable device
containing intake and exhaust pipes; permits a submarine to stay
submerged for extended periods of time [syn: snorkel, schnorkel, schnorchel, snorkel
breather]
User Contributed Dictionary
English
Pronunciation

 Rhymes: iːðə(r)
Noun
Extensive Definition
A breather is a nonlinear wave phenomenon in which energy
concentrates in a localized and oscillatory fashion. This
contradicts with the expectations derived from the corresponding
linear system for infinitesimal amplitudes, which tends
towards an even distribution of initially localized energy.
A discrete breather is a breather solution on a
nonlinear lattice.
The term breather originates from the
characteristic that most breathers are localized in space and
oscillate (breath) in
time. But also the opposite situation: oscillations in space and
localized in time, is denoted as a breather.
Overview
A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sineGordon equation are examples of onedimensional partial differential equations that possess breather solutions. Discrete nonlinear Hamiltonian lattices in many cases support breather solutions. Breathers are solitonic structures. There are two types of breathers: standing or traveling ones. Standing breathers correspond to localized solutions whose amplitude vary in time (they are sometimes called oscillons). A necessary condition for the existence of breathers in discrete lattices is that the breather main frequency and all its multipliers are located outside of the phonon spectrum of the lattice.Example of a breather solution for the sineGordon equation
The sineGordon equation is the nonlinear dispersive partial differential equation \frac  \frac + \sin u = 0,
with the field u a
function of the spatial coordinate x and time t.
An exact solution found by using the
inverse scattering transform is is the dispersive partial
differential equation:
 i\,\frac + \frac + u^2 u = 0,
with u a complex
field as a function of x and t. Further i denotes the imaginary
unit.
One of the breather solutions is
u = \left( \frac  1 \right)\; a\; \exp(i\, a^2\,
t) \quad\text\quad \theta=a^2\,b\,\sqrt\;t,
which gives breathers periodic in space x and
approaching the uniform value a when moving away from the focus
time t = 0. These breathers exist for values of the modulation parameter b less
than √ 2.
See also
References and notes
Synonyms, Antonyms and Related Words
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