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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.
2010 MATHEMATICS SUBJECT CLASSIFICATION CODES:
Acknowledgments
The authors would like to thank Professors Miriam Manoel and Gabriela Gomes for useful comments and suggestions.
Disclosure statement
No potential conflict of interest was reported by the authors.
Additional information
Funding
CMUP is supported by the European Regional Development Fund through the programme COMPETE and Portuguese Government through the Fundação para a Ciência e a Tecnologia (FCT) [project number PEst-C/MAT/UI0144/2011]; J.F. Oliveira was supported by a grant from the Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) of Brazil [grant number 202332/2011-0].