Stable manifolds for an orbitally unstable NLS
نویسنده
چکیده
By this we mean that φ > 0 and φ ∈ C2(R3). It is a classical fact (see Coffman [Cof]) that such solutions exist and are unique for the cubic nonlinearity. Moreover, they are radial and smooth. Similar facts are known for more general nonlinearities, see e.g., Berestycki and Lions [BerLio] for existence and Kwon [Kwo] for uniqueness in greater generality. Clearly, ψ = eitα 2 φ solves (1). We seek an H1-solution ψ of the form ψ = W +R where W (t, x) = eφ(x− y(t), α(t)) (3)
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