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Based on equivariant bifurcation theory, we prove existence of lattice solutions branching off the zero magnetization state and investigate their stability. We observe in particular the stabilization of quadratic vortex\u2013antivortex lattice configurations and instability of hexagonal skyrmion lattice configurations, and we illustrate our findings by numerical studies.<\/jats:p>","DOI":"10.1007\/s00332-020-09654-5","type":"journal-article","created":{"date-parts":[[2020,9,25]],"date-time":"2020-09-25T21:02:44Z","timestamp":1601067764000},"page":"3389-3420","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["Lattice Solutions in a Ginzburg\u2013Landau Model for a Chiral Magnet"],"prefix":"10.1007","volume":"30","author":[{"given":"Xinye","family":"Li","sequence":"first","affiliation":[]},{"given":"Christof","family":"Melcher","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2020,9,25]]},"reference":[{"key":"9654_CR1","first-page":"1174","volume":"5","author":"AA Abrikosov","year":"1957","unstructured":"Abrikosov, A.A.: On the magnetic properties of superconductors of the second group. 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