References
- Flach S , Gorbach A . Discrete breathers -- advances in theory and applications. Phys Rep. 2008;467:1–116.
- Aubry S . Existence, linear stability and quantization. Physica D. 1996;103:201–250.
- Flach S , Willis CR . Discrete breathers. Phys Rep. 1998;295:182–264.
- Hennig D , Tsironis GP . Wave transmission in nonlinear lattices. Phys Rep. 1999;307:335–432.
- MacKay RS , Aubry S . Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators. Nonlinearity. 1994;7:1623–1643.
- Aubry S . Discrete breathers in anharmonic models with acoustic phonons. Ann l’Inst H Poincaré (A) Phys Theor. 1998;68:381–420.
- Aubry S , Kopidakis G , Kadelburg V . Variational proof for hard Discrete breathers in some classes of Hamiltonian dynamical systems. Discrete Contin Dyn Syst B. 2001;1:271–298.
- James G . Centre manifold reduction for quasilinear discrete systems. J. Nonlinear Sci. 2003;13:27–63.
- Hennig D . Existence and non-existence of breather solutions in damped and driven non-linear lattices. AIP Adv. 2013;3:102127.1–102127.10.
- Bambusi D . Exponential stability of breathers in Hamiltonian networks of weakly coupled oscillators. Nonlinearity. 1996;9:433–457.
- Sepulchre JA , MacKay RS . Localized oscillations in conservative or dissipative networks of weakly coupled autonomous oscillators. Nonlinearity. 1997;10:679–713.
- Marin JL , Aubry S . Aubry, Breathers in nonlinear lattices: numerical calculation from the anticontinuous limit. Nonlinearity. 1994;9:1501–1528.
- Aubry S . Breathers in nonlinear lattices: existence, linear stability and quantization. Physica D. 1997;103:201–250.
- MacKay RS , Sepulchre JA . Stability of discrete breathers. Physica D. 1998;119:148–162.
- Marin JL , Falo F , Martinez PJ , et al . Discrete breathers in dissipative lattices. Phys Rev E. 2001;63:066603.
- Martinez PJ , Meister M , Floria LM , et al . Discrete breathers in dissipative lattices. Chaos. 2003;13:610–623.
- Sato M , Hubbard BE , Sievers AJ , et al . Observation of locked intrinsic localized vibrational modes in a micromechanical oscillator array. Phys Rev Lett. 2003;90:044102.
- Sato M , Hubbard BE , English LQ , et al . Study of intrinsic localized vibrational modes in micromechanical oscillator arrays. Chaos. 2003;13:702–715.
- Sato M , Hubbard BE , Sievers AJ . Colloquium: Nonlinear energy localization and its manipulation in micromechanical oscillator arrays. Rev Mod Phys. 2006;78:137–157.
- Trias E , Mazo J , Orlando T . Discrete breathers in nonlinear lattices: experimental detection in a Josephson array. Phys Rev Lett. 2000;84:741–744.
- Binder P , Abraimov D , Ustinov AV , et al . Observation of breathers in Josephson ladders. Phys Rev Lett. 2000;84:745–748.
- Sato M , Sievers AJ . Direct observation of the discrete character of intrinsic localized modes in an antiferromagnet. Nature. 2004;432:486–488.
- Schwarz UT , English LQ , Sievers AJ . Experimental generation and observation of intrinsic localized spin wave modes in an antiferromagnet. Phys Rev Lett. 1999;83:223–226.
- Fleischer JW , Segev M , Efremidis NK , et al . Observation of two-dimensional discrete solitons in optically induced nonlinear photonic lattices. Nature. 2003;422:147–150.
- Eisenberg HS , Silberberg Y , Morantotti R , et al . Discrete spatial optical solitons in waveguide arrays. Phys Rev Lett. 1998;81:3383–3386.
- Eiermann B , Anker T , Albiez M , et al . Oberthaler, bright Bose-Einstein gap solitons of atoms with repulsive interaction. Phys Rev Lett. 2004;92:23041.
- Cuevas J , English LQ , Kevredikis PG , et al . Discrete breathers in a forced-damped array of coupled pendula: modeling, computation, and experiment. Phys Rev Lett. 2009;102:224101.
- Palmero F , English LQ , Cuevas J , et al . Discrete breathers in a nonlinear electric line: modeling, computation, and experiment. Phys Rev E. 2011;84:026605.
- Boechler N , Theocharis G , Job S , et al . Discrete breathers in one-dimensional diatomic granular crystals. Phys Rev Lett. 2010;104:244302.
- Remoissenet M . Waves called solitons: concepts and experiments. Berlin: Springer-Verlag; 2003.
- Morgante AM , Johansson M , Kopidakis G , et al . Standing wave instabilities in a chain of nonlinear coupled oscillators. Physica D. 2002;162:53–94.
- Smart DR . Fixed point theorems. Cambridge: Cambridge University Press; 1973.
- DeVito C . Functional analysis and linear operator theory. Reading (MA): Addison-Wesley; 1990.
- Bocarra N . Functional analysis. New York (NY): Academic Press; 1990.
- Zeidler E . Applied functional analysis. New York (NY): Springer-Verlag; 1995.
- Eilbeck JC , Lomdahl PS , Scott AC . The discrete self-trapping equation. Physica D. 1985;16:318–338.
- Flach S . Breathers on lattices with long range interaction. Phys Rev E. 1998;58:R4116–R4119.