[{"publication_status":"published","external_id":{"arxiv":["1702.04413"]},"das_tickbox":"1","author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"first_name":"Jason","last_name":"Murphy","full_name":"Murphy, Jason"},{"full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","first_name":"Monica","last_name":"Visan"}],"month":"01","abstract":[{"lang":"eng","text":"We consider the initial-value problem for the cubic-quintic nonlinear Schrödinger equation (π‘–πœ•π‘‘+Ξ”)β’πœ“ =𝛼1β’πœ“ βˆ’π›Ό3⁒|πœ“|2β’πœ“ +𝛼5⁒|πœ“|4β’πœ“ in three spatial dimensions in the class of solutions with |πœ“β‘(π‘₯)| →𝑐 >0 as |π‘₯| β†’βˆž. Here 𝛼1, 𝛼3, 𝛼5, and 𝑐 are such that πœ“β‘(π‘₯) ≑𝑐 is an energetically stable equilibrium solution to this equation. Normalizing the boundary condition to πœ“β‘(π‘₯) β†’1 as |π‘₯| β†’βˆž, we study the associated initial-value problem for 𝑒 =πœ“ βˆ’1 and prove a scattering result for small initial data in a weighted Sobolev space."}],"volume":50,"date_created":"2026-06-19T07:49:03Z","date_published":"2018-01-01T00:00:00Z","year":"2018","article_type":"original","intvolume":" 50","issue":"3","oa":1,"language":[{"iso":"eng"}],"article_processing_charge":"No","arxiv":1,"extern":"1","type":"journal_article","mathsc":["35Q55"],"user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","scopus_import":"1","page":"2681-2739","status":"public","doi":"10.1137/17m1116702","publication_identifier":{"issn":["0036-1410","1095-7154"]},"quality_controlled":"1","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","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1702.04413"}],"publisher":"Society for Industrial & Applied Mathematics","publication":"SIAM Journal on Mathematical Analysis","keyword":["cubic-quintic NLS","nonvanishing boundary conditions","space-time resonances","scattering"],"citation":{"short":"R. Killip, J. Murphy, M. Vişan, SIAM Journal on Mathematical Analysis 50 (2018) 2681–2739.","chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. β€œThe Initial-Value Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” SIAM Journal on Mathematical Analysis. Society for Industrial & Applied Mathematics, 2018. https://doi.org/10.1137/17m1116702.","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.","ama":"Killip R, Murphy J, Vişan M. The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions. SIAM Journal on Mathematical Analysis. 2018;50(3):2681-2739. doi:10.1137/17m1116702","ieee":"R. Killip, J. Murphy, and M. Vişan, β€œThe initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions,” SIAM Journal on Mathematical Analysis, vol. 50, no. 3. Society for Industrial & Applied Mathematics, pp. 2681–2739, 2018.","apa":"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. Society for Industrial & Applied Mathematics. https://doi.org/10.1137/17m1116702","mla":"Killip, Rowan, et al. β€œThe Initial-Value Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” SIAM Journal on Mathematical Analysis, vol. 50, no. 3, Society for Industrial & Applied Mathematics, 2018, pp. 2681–739, doi:10.1137/17m1116702."}}]