Projections of Patterns and Mode Interactions

2017/03/30 by Sofia S. B. S. D. Castro, Sofia B. S. D. Castro, Isabel S. Labouriau +4
Computer Science · Mathematics · Physics and Astronomy · #37G40 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Theoretical and Computational Physics #math.DS #msc:37G40

paper · pdf · doi:10.48550/arxiv.1703.10635

openalex publication_date 2017/03/30 · arxiv created 2017/11/03 · arxiv updated 2017/11/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study solutions of bifurcation problems with periodic boundary conditions, with periods in an n+1-dimensional lattice and their projection into n-dimensional space through integration of the last variable. We show that generically the projection of a single mode solution is a mode interaction. This can be applied to the study of black-eye patterns.

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