# Bifurcation of relative equilibria in infinite-dimensional Hamiltonian systems

Relative equilibria in perturbed infinite-dimensional Hamiltonian systems are studied. We assume that the unperturbed system has symmetry and relative equilibria, and some of symmetries are broken by the perturbations. A sufficient condition for persistence of relative equilibia is obtained by Kapitula et. al. [cf. Physica D, 195 (2004)]. When this condition is not satisfied, we detect saddle-node and pitchfork bifurcations along with the linear stability of 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 Kazuyuki Yagasaki.