Breather

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Breather or discrete breather, is phenomenon in which energy piles up in an irregular and non-linear fashion, rather than dispersing evenly, as one might expect it to do. ^[1]

A breather is a localized periodic solution of either continuous media equations or discrete lattice equations. The exactly solvable sine-Gordon one dimensional PDE possesses breather solutions. Discrete nonlinear Hamiltonian lattices in many cases support breather solutions. Breathers are closely related to solitonic structures, and meanwhile solitons are travaling solution, breathers correspond to localized solutions whose amplitude vary in time (they are sometimes called oscillons). A necessary condition for breather existence in discrete lattices is that the breather main frequency and all its multipliers are located outside of the phonon spectrum of the lattice.