Odd H^1 solutions to 1D semilinear NLS, NLS with potential, and defocusing Hartree equations decay locally in space as t→∞ via virial identities, covering subcritical to supercritical long-range cases.
Cuccagna, The Hamiltonian Structure of the Nonlinear Schrödinger Equa tion and the Asymptotic Stability of its Ground States , Commun
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Decay of small odd solutions for long range Schr\"odinger and Hartree equations in one dimension
Odd H^1 solutions to 1D semilinear NLS, NLS with potential, and defocusing Hartree equations decay locally in space as t→∞ via virial identities, covering subcritical to supercritical long-range cases.