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| Breathers are considered a rare phenomenon for constant coefficient nonlinear wave equations. Recently, a nonlinear wave equation with spatially periodic step potentials has been found to support breathers by using a combination of spatial dynamics, center manifold reduction and bifurcation theory. Via inverse spectral theory for weighted Sturm-Liouville equations, we characterize a larger class of potentials that allow breathers. The research is motivated by the quest of using photonic crystals as optical storage. |
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