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Proof of existence of breathers for time-reversible or Hamiltonian networks of weakly coupled oscillators. (English) Zbl 0811.70017

Summary: Existence of ‘breathers’, that is, time-periodic, spatially localized solutions, is proved for a broad range of time-reversible or Hamiltonian networks of weakly coupled oscillators. Some of their properties are discussed, some generalizations suggested, and several open questions raised.

MSC:

70K99 Nonlinear dynamics in mechanics
34A12 Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations
34C25 Periodic solutions to ordinary differential equations
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