Bifurcations of relative equilibria in perturbed infinite-dimensional Hamiltonian systems are studied. We assume that the unperturbed systems have symmetries and some of them are broken by the perturbations. We detect saddle-node and pitchfork bifurcations along with the linear stability of bifurcated relative equilibria. In this talk, we will illustrate our results and show an application to solitary waves of the nonlinear Schr\"odinger equations.
This is a joint work with Prof. Kazuyuki Yagasaki.