We prove the existence of the scattering operator in the neighborhood of the origin in the weighted Sobolev space Hβ, 1 with β = max (frac(3, 2), 1 + frac(2, n)) for the nonlinear Klein-Gordon equation with a power nonlinearityut t - Δ u + u = μ | u |σ - 1 u, (t, x) ∈ R × Rn, where 1 + frac(4, n + 2) < σ < 1 + frac(4, n) for n ≥ 3, μ ∈ C.
- Asymptotics of solutions
- Higher space dimensions
- Nonlinear Klein-Gordon equations
- Power nonlinearities
- Scattering operator