The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions Killip, Rowan Murphy, Jason Visan, Monica cubic-quintic NLS nonvanishing boundary conditions space-time resonances scattering We consider the initial-value problem for the cubic-quintic nonlinear Schrödinger equation (𝑖𝜕𝑡+Δ)⁢𝜓 =𝛼1⁢𝜓 −𝛼3⁢|𝜓|2⁢𝜓 +𝛼5⁢|𝜓|4⁢𝜓 in three spatial dimensions in the class of solutions with |𝜓⁡(𝑥)| →𝑐 >0 as |𝑥| →∞. Here 𝛼1, 𝛼3, 𝛼5, and 𝑐 are such that 𝜓⁡(𝑥) ≡𝑐 is an energetically stable equilibrium solution to this equation. Normalizing the boundary condition to 𝜓⁡(𝑥) →1 as |𝑥| →∞, we study the associated initial-value problem for 𝑢 =𝜓 −1 and prove a scattering result for small initial data in a weighted Sobolev space. Society for Industrial & Applied Mathematics 2018 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22045 Killip R, Murphy J, Vişan M. The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>SIAM Journal on Mathematical Analysis</i>. 2018;50(3):2681-2739. doi:<a href="https://doi.org/10.1137/17m1116702">10.1137/17m1116702</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1137/17m1116702 info:eu-repo/semantics/altIdentifier/issn/0036-1410 info:eu-repo/semantics/altIdentifier/issn/1095-7154 info:eu-repo/semantics/altIdentifier/arxiv/1702.04413 info:eu-repo/semantics/openAccess