Isolated patches of spatially oscillating pattern have been found to emerge near a pattern-
forming instability in a wide variety of experiments and mathematical models. However …

The emergence of localized radial patterns from a Turing instability has been well studied in
two-and three-dimensional settings and predicted for higher spatial dimensions. We prove …

Localised patterns are often observed in models for dryland vegetation, both as peaks of
vegetation in a desert state and as gaps within a vegetated state, known as 'fairy circles' …

In this article, we develop a method to perform constructive proofs of existence of smooth
planar localized patterns in the Gray-Scott model. Specifically, we construct a natural Hilbert …

Spatially localized patterns offer fascinating insights into the emergence of organized
behaviors, from weather fronts and desert vegetation to stop-and-go traffic waves and the …

This paper is concerned with complex Banach-space valued functions of the form $$\hat {f}
_k (r\cos\theta, r\sin\theta, z)=\mathrm {e}^{\mathrm {i} k\theta} f_k (r, z),\qquad r\in …