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.
Klaus, On the Bound State of Schrödinger Operators in One Dimension , Annals of Physics 108 (1977), pp
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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.