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.
@article{arxiv.1703.10635,
title = {Projections of Patterns and Mode Interactions},
author = {Sofia B. S. D. Castro and Isabel S. Labouriau and Juliane F. Oliveira},
journal= {arXiv preprint arXiv:1703.10635},
year = {2017}
}