| Abstract: |
| Motivated by the quest to develop optical storage, we investigate the formation and persistence of breathers in materials with periodically varying properties in the presence of randomness, noise, and damping. A particular focus is on whether appropriately chosen forcing can extend the lifetime of these long-lived structures. Our work builds on the rigorous construction of breathers for a Klein-Gordon equation with periodically varying coefficients and is further motivated by recent results suggesting that such breathers are typically unstable. In this presentation, we explore the extent to which randomness, noise, damping, and forcing can mitigate, delay, or even counteract this instability. Since their stability is notoriously difficult to address analytically, numerical stability analysis is essential. At the same time, the resulting numerical schemes naturally lead to lattice equations whose relationship to the underlying continuum description is rather delicate. |
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