Artículo de revista
Decay of small odd solutions for long range Schrödinger and Hartree equations in one dimension
Date
2020Registration in:
Nonlinearity 33 (2020) 1156–1182
10.1088/1361-6544/ab591c
Author
Martínez, María E.
Institutions
Abstract
We consider the long time asymptotics of (not necessarily small) odd solutions
to the nonlinear Schrödinger equation with semi-linear and nonlocal Hartree
nonlinearities, in one dimension of space. We assume data in the energy space
H1(R) only, and we prove decay to zero in compact regions of space as time
tends to infinity. We give three different results where decay holds: semilinear
NLS, NLS with a suitable potential, and defocusing Hartree. The proof is
based on the use of suitable virial identities, in the spirit of nonlinear Klein–
Gordon models (Kowalczyk et al 2017 Lett. Math. Phys. 107 921–31), and
covers scattering sub, critical and supercritical (long range) nonlinearities. No
spectral assumptions on the NLS with potential are needed.