3 problems

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McCalla–Sandstede conjecture on collapse of the upper snaking branch
Consider the upper snaking branch of localized axisymmetric patterns, whose spatially periodic patches (SPPs) are added near the core of the pattern, namely near $r=0$ , rather than…
Conjectureopenbifurcation-theory localized-patterns snakingarXiv posted 2 days ago
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The periodic-limit conjecture for localized patterns in the quintic Swift–Hohenberg equation
The quintic Swift–Hohenberg (SH) equation is the stationary planar equation obtained by including a quintic nonlinearity in the Swift–Hohenberg model. A localized pattern is a spat…
Conjectureopenlocalized-patterns periodic-solutions swift-hohenberg-equationarXiv posted 2 days ago
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Sparse-coupling saddle-node conjecture for snaking curves on ring lattices
Let $N$ be the number of nodes in a ring lattice, and let $m$ denote the interaction-length parameter for sparse coupling, with nearest-neighbour and next-nearest-neighbour couplin…
Conjectureopenbifurcation-theory lattice-dynamical-systems localized-patternsarXiv posted 2 days ago

McCalla–Sandstede conjecture on collapse of the upper snaking branch