{"month":"01","abstract":[{"lang":"eng","text":"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."}],"volume":50,"date_created":"2026-06-19T07:49:03Z","year":"2018","article_type":"original","date_published":"2018-01-01T00:00:00Z","intvolume":"        50","issue":"3","oa":1,"language":[{"iso":"eng"}],"publication_status":"published","external_id":{"arxiv":["1702.04413"]},"das_tickbox":"1","author":[{"first_name":"Rowan","last_name":"Killip","full_name":"Killip, Rowan"},{"full_name":"Murphy, Jason","first_name":"Jason","last_name":"Murphy"},{"id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica","last_name":"Visan","first_name":"Monica"}],"day":"01","OA_type":"green","date_updated":"2026-06-25T07:49:21Z","_id":"22045","title":"The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions","OA_place":"repository","publisher":"Society for Industrial & Applied Mathematics","main_file_link":[{"url":"https://doi.org/10.48550/arXiv.1702.04413","open_access":"1"}],"citation":{"apa":"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>","mla":"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>.","ieee":"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.","ama":"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>","ista":"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.","chicago":"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>.","short":"R. Killip, J. Murphy, M. Vişan, SIAM Journal on Mathematical Analysis 50 (2018) 2681–2739."},"keyword":["cubic-quintic NLS","nonvanishing boundary conditions","space-time resonances","scattering"],"publication":"SIAM Journal on Mathematical Analysis","arxiv":1,"article_processing_charge":"No","type":"journal_article","extern":"1","mathsc":["35Q55"],"page":"2681-2739","scopus_import":"1","oa_version":"Preprint","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","status":"public","quality_controlled":"1","publication_identifier":{"issn":["0036-1410","1095-7154"]},"doi":"10.1137/17m1116702"}