Pinning and dipole asymptotics of locally deformed striped phases

Autor:	Scheel, Arnd, Wu, Qiliang
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs Nonlinear Sciences - Pattern Formation and Solitons
Druh dokumentu:	Working Paper
Popis:	We investigate the effect of spatial inhomogeneity on perfectly periodic, self-organized striped patterns in spatially extended systems. We demonstrate that inhomogeneities select a specific translate of the striped patterns and induce algebraically decaying, dipole-type farfield deformations. Phase shifts and leading order terms are determined by effective moments of the spatial inhomogeneity. Farfield decay is proportional to the derivatives of the Green's function of an effective Laplacian. Technically, we use mode filters and conjugacies to an effective Laplacian to establish Fredholm properties of the linearization in Kondratiev spaces. Spatial localization in a contraction argument is gained through the use of an explicit deformation ansatz and a subtle cancellation in Bloch wave space. Comment: 30p
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2405.20265 Zobrazit plný text záznamu View this record from Arxiv