article published yes Rowan Killip author Jason Murphy author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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 Mathematics2018 eng cubic-quintic NLSnonvanishing boundary conditionsspace-time resonancesscattering 0036-1410 1095-7154 1702.0441310.1137/17m1116702 5032681-2739 yes Killip, Rowan, et al. “The Initial-Value Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3, Society for Industrial &#38; Applied Mathematics, 2018, pp. 2681–739, doi:<a href="https://doi.org/10.1137/17m1116702">10.1137/17m1116702</a>. Killip, R., Murphy, J., &#38; Vişan, M. (2018). The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics. <a href="https://doi.org/10.1137/17m1116702">https://doi.org/10.1137/17m1116702</a> R. Killip, J. Murphy, and M. Vişan, “The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions,” <i>SIAM Journal on Mathematical Analysis</i>, vol. 50, no. 3. Society for Industrial &#38; Applied Mathematics, pp. 2681–2739, 2018. 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> Killip R, Murphy J, Vişan M. 2018. The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions. SIAM Journal on Mathematical Analysis. 50(3), 2681–2739. Killip, Rowan, Jason Murphy, and Monica Vişan. “The Initial-Value Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>SIAM Journal on Mathematical Analysis</i>. Society for Industrial &#38; Applied Mathematics, 2018. <a href="https://doi.org/10.1137/17m1116702">https://doi.org/10.1137/17m1116702</a>. R. Killip, J. Murphy, M. Vişan, SIAM Journal on Mathematical Analysis 50 (2018) 2681–2739. 220452026-06-19T07:49:03Z2026-06-25T07:49:21Z