Stability of waves in perturbed Hamiltonian systems

The effects of Hamiltonian perturbations of Hamiltonian systems, in which the perturbation destroys some of the symmetries of the original system, is studied. Using a combination of Lyapunov–Schmidt theory and the Evans function, the existence and stability of waves is determined. It is demonstrated that the location of the nonzero eigenvalues due to the symmetry-breaking perturbation is intimately related to the features of a reduced energy surface. The theoretical results are applied to systems describing the propagation of waves in a weakly inhomogeneous media.