| Abstract: |
| 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. Using the Lyapunov-Schmidt method,
we detect saddle-node and pitchfork bifurcations along with
the linear stability of bifurcated relative equilibria. Our
theory is illustrated for solitary waves of the nonlinear
Schr\{o}dinger equations and the theoretical results are
demonstrated with the numerical ones. |
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