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arXiv · 2507.12277

Branches of localized patterned states

Bjorn Sandstede
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Abstract

Motivated by theoretical analyses of spatially localized structures with arbitrarily long periodic plateaus, we provide a framework of assumptions that simplifies their analysis and leads to a topological criterion for when localized patterned structures lie on a discrete stack of loops or on a single unbounded branch. The framework proposed here also connects closely with continuation algorithms that are often used to verify the hypotheses that guarantee the emergence of localized patterned states.

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Bjorn Sandstede. 2025-07-16. Branches of localized patterned states. https://arxiv.org/abs/2507.12277

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