We consider the non-linear Hartree equation with a slowly varying external potential Vε and a short range, attractive two-body interaction W. We prove the existence of stationary solutions which are approximatively given by a superposition of several Hartree solitons with their center of mass positions behaving, at the leading order, as classical particles at rest in the background potential Vε.
Stationary solutions for the non-linear Hartree equation with a slowly varying potential
MACRI', MARTA;NOLASCO, MARGHERITA
2009-01-01
Abstract
We consider the non-linear Hartree equation with a slowly varying external potential Vε and a short range, attractive two-body interaction W. We prove the existence of stationary solutions which are approximatively given by a superposition of several Hartree solitons with their center of mass positions behaving, at the leading order, as classical particles at rest in the background potential Vε.File in questo prodotto:
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