[{"type":"report","title":"Bifurcations of nontrivial solutions of a cubic Helmholtz system","issued":{"date-parts":[["2018"]]},"DOI":"10.5445\/IR\/1000087314","author":[{"family":"Mandel","given":"Rainer"},{"family":"Scheider","given":"Dominic"}],"publisher":"Karlsruher Institut f\u00fcr Technologie (KIT)","ISSN":"2365-662X","collection-title":"CRC 1173","abstract":"This paper presents local and global bifurcation results for radially symmetric solutions of the cubic Helmholtz system \r\n$\\begin{equation*}\r\n\\begin{cases} -\u0394u - \u03bcu = \\left( u^2 + b \\: v^2 \\right) u &\\text{ on }\r\n\\mathbb{R}^3, \\\\ -\u0394v - \u03bdv = \\left( v^2 + b \\: u^2 \\right) v &\\text{ on\r\n} \\mathbb{R}^3. \\end{cases} \\end{equation*}$\r\nIt is shown that every point along any given branch of radial semitrivial solutions $(u_0, 0, b)$ or diagonal solutions $(ub,ub,b)$ (for $\u03bc=\u03bd)$ is a bifurcation point. Our analysis is based on a detailed investigation of the oscillatory behavior of solutions at infinity that are shown to decay like $\\frac{1}{|x|}$ as $|x|\\to\\infty$.","keyword":"nonlinear Helmholtz sytem, bifurcation","number-of-pages":31,"kit-publication-id":"1000087314"}]