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<p>We prove the existence of time-localized and spatially periodic solutions for systems of coupled nonlinear oscillators, i.e. Klein–Gordon lattices. Compared to common discrete breathers, as time-periodic and spatially localized solutions, the role of time and space is exchanged. For the existence proofs of time-localized and space periodic solutions respectively space periodic solutions with a desired degree of exponential time-localization, two versions of Schauder’s fixed point theorem are utilized. For weakly coupled oscillators the concept of of continuation of solutions from the anti-integrable limit is used for the existence proof. Furthermore, we prove the existence of solutions that are localized in time as well as space.</p>

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Time-localized solutions in nonlinear Klein–Gordon lattices

  • 期刊论文

  • 发表日期：

    2026年4月29日

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  • Dirk Hennig,
  • Christos Sourdis

摘要

We prove the existence of time-localized and spatially periodic solutions for systems of coupled nonlinear oscillators, i.e. Klein–Gordon lattices. Compared to common discrete breathers, as time-periodic and spatially localized solutions, the role of time and space is exchanged. For the existence proofs of time-localized and space periodic solutions respectively space periodic solutions with a desired degree of exponential time-localization, two versions of Schauder’s fixed point theorem are utilized. For weakly coupled oscillators the concept of of continuation of solutions from the anti-integrable limit is used for the existence proof. Furthermore, we prove the existence of solutions that are localized in time as well as space.