Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3 Killip, Rowan Oh, Tadahiro Pocovnicu, Oana Visan, Monica We consider the cubic–quintic nonlinear Schrödinger equation: (mathematical formular) In the first part of the paper, we analyze the one-parameter family of ground state solitons associated to this equation with particular attention to the shape of the associated mass/energy curve. Additionally, we are able to characterize the kernel of the linearized operator about such solitons and to demonstrate that they occur as optimizers for a one-parameter family of inequalities of Gagliardo–Nirenberg type. Building on this work, in the latter part of the paper we prove that scattering holds for solutions belonging to the region R of the mass/energy plane where the virial is positive. We show that this region is partially bounded by solitons also by rescalings of solitons (which are not soliton solutions in their own right). The discovery of rescaled solitons in this context is new and highlights an unexpected limitation of any virial-based methodology. Springer Nature 2017 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22071 Killip R, Oh T, Pocovnicu O, Vişan M. Solitons and scattering for the cubic-quintic nonlinear Schrödinger equation on R^3. <i>Archive for Rational Mechanics and Analysis</i>. 2017;225:469-548. doi:<a href="https://doi.org/10.1007/s00205-017-1109-0">10.1007/s00205-017-1109-0</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1007/s00205-017-1109-0 info:eu-repo/semantics/altIdentifier/issn/0003-9527 info:eu-repo/semantics/altIdentifier/e-issn/1432-0673 info:eu-repo/semantics/altIdentifier/arxiv/1409.6734 info:eu-repo/semantics/openAccess