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We consider the long time asymptotics of (not necessarily small) oddsolutions to the nonlinear Schr\"odinger equation with semi-linear and nonlocalHartree nonlinearities, in one dimension of space. We assume data in the energyspace $H^1(\mathbb{R})$ only, and we prove decay to zero in compact regions ofspace as time tends to infinity. We give three different results where decayholds: semilinear NLS, NLS with a suitable potential, and defocusing Hartree.The proof is based on the use of suitable virial identities, in the spirit ofnonlinear Klein-Gordon models as in Kowalczyk-Martel-Mu\~noz, and coversscattering sub, critical and supercritical (long range) nonlinearities. Nospectral assumptions on the NLS with potential are needed.

Decay of small odd solutions for long range Schr\"odinger and Hartree equations in one dimension