Abstract
The orbital stability of standing waves for semilinear wave equations is studied in the case that the energy is indefinite and the underlying space domain is bounded or a compact manifold or whole R n with n ⩾ 2 . The stability is determined by the convexity on ω of the lowest energy d ( ω ) of standing waves with frequency ω. The arguments rely on the conservation of energy and charge and the construction of suitable invariant manifolds of solution flows.
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