Bifurcations of nontrivial solutions of a cubic Helmholtz system (Q2281668)

The authors study the cubic Helmholtz system given by \[ \begin{cases} -\Delta u - \mu u = \left(u^2+bv^2\right)u &\text{on }\mathbb{R}^3,\\ -\Delta v - \nu v = \left(v^2+bu^2\right)v &\text{on }\mathbb{R}^3, \end{cases} \] and prove local and global bifurcation results for radially symmetric solutions of such systems. Based on a detailed investigation of the oscillatory behavior and the decay of solutions at infinity, it is shown that every point along any given branch of radial semitrivial solutions \((u_0,0,b)\) or diagonal solutions \((u_b,u_b,b)\) (for \(\mu=\nu\)) is a bifurcation point.