[{"year":"2023","day":"09","date_updated":"2026-06-25T07:54:44Z","publisher":"IOP Publishing","article_type":"original","publication_status":"published","status":"public","keyword":["Ablowitz–Ladik","continuum limit","cubic NLS"],"intvolume":"        36","extern":"1","author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"first_name":"Zhimeng","last_name":"Ouyang","full_name":"Ouyang, Zhimeng"},{"first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"},{"full_name":"Wu, Lei","first_name":"Lei","last_name":"Wu"}],"OA_type":"green","date_published":"2023-06-09T00:00:00Z","oa_version":"Preprint","oa":1,"OA_place":"repository","quality_controlled":"1","language":[{"iso":"eng"}],"issue":"7","type":"journal_article","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","month":"06","citation":{"apa":"Killip, R., Ouyang, Z., Vişan, M., &#38; Wu, L. (2023). Continuum limit for the Ablowitz–Ladik system. <i>Nonlinearity</i>. IOP Publishing. <a href=\"https://doi.org/10.1088/1361-6544/acd978\">https://doi.org/10.1088/1361-6544/acd978</a>","ista":"Killip R, Ouyang Z, Vişan M, Wu L. 2023. Continuum limit for the Ablowitz–Ladik system. Nonlinearity. 36(7), 3751–3775.","ama":"Killip R, Ouyang Z, Vişan M, Wu L. Continuum limit for the Ablowitz–Ladik system. <i>Nonlinearity</i>. 2023;36(7):3751-3775. doi:<a href=\"https://doi.org/10.1088/1361-6544/acd978\">10.1088/1361-6544/acd978</a>","chicago":"Killip, Rowan, Zhimeng Ouyang, Monica Vişan, and Lei Wu. “Continuum Limit for the Ablowitz–Ladik System.” <i>Nonlinearity</i>. IOP Publishing, 2023. <a href=\"https://doi.org/10.1088/1361-6544/acd978\">https://doi.org/10.1088/1361-6544/acd978</a>.","short":"R. Killip, Z. Ouyang, M. Vişan, L. Wu, Nonlinearity 36 (2023) 3751–3775.","ieee":"R. Killip, Z. Ouyang, M. Vişan, and L. Wu, “Continuum limit for the Ablowitz–Ladik system,” <i>Nonlinearity</i>, vol. 36, no. 7. IOP Publishing, pp. 3751–3775, 2023.","mla":"Killip, Rowan, et al. “Continuum Limit for the Ablowitz–Ladik System.” <i>Nonlinearity</i>, vol. 36, no. 7, IOP Publishing, 2023, pp. 3751–75, doi:<a href=\"https://doi.org/10.1088/1361-6544/acd978\">10.1088/1361-6544/acd978</a>."},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2206.02720"}],"_id":"22046","publication_identifier":{"eissn":["1361-6544"],"issn":["0951-7715"]},"das_tickbox":"1","date_created":"2026-06-19T07:49:24Z","doi":"10.1088/1361-6544/acd978","external_id":{"arxiv":["2206.02720"]},"page":"3751-3775","article_processing_charge":"No","arxiv":1,"title":"Continuum limit for the Ablowitz–Ladik system","volume":36,"mathsc":["35Q55","37K05","37K10"],"abstract":[{"lang":"eng","text":"We show that solutions to the Ablowitz–Ladik system converge to solutions of the cubic nonlinear Schrödinger equation for merely L2 initial data. Furthermore, we consider initial data for this lattice model that excites Fourier modes near both critical points of the discrete dispersion relation and demonstrate convergence to a decoupled system of nonlinear Schrödinger equations."}],"publication":"Nonlinearity"},{"extern":"1","intvolume":"        50","keyword":["cubic-quintic NLS","nonvanishing boundary conditions","space-time resonances","scattering"],"date_published":"2018-01-01T00:00:00Z","OA_type":"green","author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Murphy, Jason","last_name":"Murphy","first_name":"Jason"},{"first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}],"day":"01","year":"2018","status":"public","publication_status":"published","publisher":"Society for Industrial & Applied Mathematics","article_type":"original","date_updated":"2026-06-25T07:49:21Z","arxiv":1,"external_id":{"arxiv":["1702.04413"]},"article_processing_charge":"No","page":"2681-2739","publication":"SIAM Journal on Mathematical Analysis","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."}],"mathsc":["35Q55"],"volume":50,"title":"The initial-value problem for the cubic-quintic NLS with nonvanishing boundary conditions","issue":"3","quality_controlled":"1","language":[{"iso":"eng"}],"OA_place":"repository","oa":1,"oa_version":"Preprint","date_created":"2026-06-19T07:49:03Z","doi":"10.1137/17m1116702","publication_identifier":{"issn":["0036-1410","1095-7154"]},"_id":"22045","das_tickbox":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1702.04413"}],"scopus_import":"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>","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. <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>","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.","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.","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>."},"month":"01","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","type":"journal_article"},{"quality_controlled":"1","language":[{"iso":"eng"}],"issue":"7","OA_place":"repository","oa_version":"Preprint","oa":1,"publication_identifier":{"eissn":["1948-206X"],"issn":["2157-5045"]},"_id":"22051","das_tickbox":"1","doi":"10.2140/apde.2016.9.1523","date_created":"2026-06-19T07:54:01Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1506.06151"}],"citation":{"chicago":"Killip, Rowan, Jason Murphy, and Monica Vişan. “The Final-State Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers, 2016. <a href=\"https://doi.org/10.2140/apde.2016.9.1523\">https://doi.org/10.2140/apde.2016.9.1523</a>.","ama":"Killip R, Murphy J, Vişan M. The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>Analysis &#38; PDE</i>. 2016;9(7):1523-1574. doi:<a href=\"https://doi.org/10.2140/apde.2016.9.1523\">10.2140/apde.2016.9.1523</a>","ieee":"R. Killip, J. Murphy, and M. Vişan, “The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions,” <i>Analysis &#38; PDE</i>, vol. 9, no. 7. Mathematical Sciences Publishers, pp. 1523–1574, 2016.","mla":"Killip, Rowan, et al. “The Final-State Problem for the Cubic-Quintic NLS with Nonvanishing Boundary Conditions.” <i>Analysis &#38; PDE</i>, vol. 9, no. 7, Mathematical Sciences Publishers, 2016, pp. 1523–74, doi:<a href=\"https://doi.org/10.2140/apde.2016.9.1523\">10.2140/apde.2016.9.1523</a>.","short":"R. Killip, J. Murphy, M. Vişan, Analysis &#38; PDE 9 (2016) 1523–1574.","apa":"Killip, R., Murphy, J., &#38; Vişan, M. (2016). The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/apde.2016.9.1523\">https://doi.org/10.2140/apde.2016.9.1523</a>","ista":"Killip R, Murphy J, Vişan M. 2016. The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions. Analysis &#38; PDE. 9(7), 1523–1574."},"scopus_import":"1","type":"journal_article","month":"11","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","arxiv":1,"external_id":{"arxiv":["1506.06151"]},"page":"1523-1574","article_processing_charge":"No","volume":9,"mathsc":["35Q55"],"abstract":[{"lang":"eng","text":"We construct solutions with prescribed scattering state to the cubic-quintic NLS (mathematical formular)in three spatial dimensions in the class of solutions with (mathematical formular). This models disturbances in an infinite expanse of (quantum) fluid in its quiescent state— the limiting modulus c corresponds to a local minimum in the energy density.\r\nOur arguments build on work of Gustafson, Nakanishi, and Tsai on the (defocusing) Gross–Pitaevskii equation. The presence of an energy-critical nonlinearity and changes in the geometry of the energy\r\nfunctional add several new complexities. One new ingredient in our argument is a demonstration that\r\nsolutions of such (perturbed) energy-critical equations exhibit continuous dependence on the initial data\r\nwith respect to the weak topology on H1/x."}],"publication":"Analysis & PDE","title":"The final-state problem for the cubic-quintic NLS with nonvanishing boundary conditions","day":"07","year":"2016","publication_status":"published","status":"public","publisher":"Mathematical Sciences Publishers","article_type":"original","date_updated":"2026-06-25T08:23:10Z","extern":"1","intvolume":"         9","keyword":["final-state problem","wave operators","cubic-quintic NLS","nonvanishing boundary conditions"],"date_published":"2016-11-07T00:00:00Z","OA_type":"green","author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"full_name":"Murphy, Jason","last_name":"Murphy","first_name":"Jason"},{"first_name":"Monica","last_name":"Visan","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca"}]},{"page":"969-986","external_id":{"arxiv":["1112.1354"]},"article_processing_charge":"No","arxiv":1,"title":"Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions","volume":19,"mathsc":["35Q55"],"abstract":[{"text":"We consider the Gross–Pitaevskii equation on R^4 and the cubic-quintic nonlinear Schrödinger equation (NLS) on R^3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.","lang":"eng"}],"publication":"Mathematical Research Letters","oa":1,"oa_version":"Preprint","OA_place":"repository","language":[{"iso":"eng"}],"quality_controlled":"1","issue":"5","type":"journal_article","month":"03","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","citation":{"apa":"Killip, R., Oh, T., Pocovnicu, O., &#38; Vişan, M. (2013). Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions. <i>Mathematical Research Letters</i>. International Press of Boston. <a href=\"https://doi.org/10.4310/mrl.2012.v19.n5.a1\">https://doi.org/10.4310/mrl.2012.v19.n5.a1</a>","ista":"Killip R, Oh T, Pocovnicu O, Vişan M. 2013. Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions. Mathematical Research Letters. 19(5), 969–986.","chicago":"Killip, Rowan, Tadahiro Oh, Oana Pocovnicu, and Monica Vişan. “Global Well-Posedness of the Gross–Pitaevskii and Cubic-Quintic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Conditions.” <i>Mathematical Research Letters</i>. International Press of Boston, 2013. <a href=\"https://doi.org/10.4310/mrl.2012.v19.n5.a1\">https://doi.org/10.4310/mrl.2012.v19.n5.a1</a>.","ama":"Killip R, Oh T, Pocovnicu O, Vişan M. Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions. <i>Mathematical Research Letters</i>. 2013;19(5):969-986. doi:<a href=\"https://doi.org/10.4310/mrl.2012.v19.n5.a1\">10.4310/mrl.2012.v19.n5.a1</a>","mla":"Killip, Rowan, et al. “Global Well-Posedness of the Gross–Pitaevskii and Cubic-Quintic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Conditions.” <i>Mathematical Research Letters</i>, vol. 19, no. 5, International Press of Boston, 2013, pp. 969–86, doi:<a href=\"https://doi.org/10.4310/mrl.2012.v19.n5.a1\">10.4310/mrl.2012.v19.n5.a1</a>.","ieee":"R. Killip, T. Oh, O. Pocovnicu, and M. Vişan, “Global well-posedness of the Gross–Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions,” <i>Mathematical Research Letters</i>, vol. 19, no. 5. International Press of Boston, pp. 969–986, 2013.","short":"R. Killip, T. Oh, O. Pocovnicu, M. Vişan, Mathematical Research Letters 19 (2013) 969–986."},"scopus_import":"1","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.1112.1354"}],"_id":"22053","publication_identifier":{"eissn":["1945-001X"],"issn":["1073-2780"]},"das_tickbox":"1","doi":"10.4310/mrl.2012.v19.n5.a1","date_created":"2026-06-19T07:54:49Z","keyword":["NLS","Gross–Pitaevskii equation","non-vanishing boundary condition"],"intvolume":"        19","extern":"1","author":[{"last_name":"Killip","first_name":"Rowan","full_name":"Killip, Rowan"},{"first_name":"Tadahiro","last_name":"Oh","full_name":"Oh, Tadahiro"},{"first_name":"Oana","last_name":"Pocovnicu","full_name":"Pocovnicu, Oana"},{"last_name":"Visan","first_name":"Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica"}],"OA_type":"green","date_published":"2013-03-15T00:00:00Z","year":"2013","day":"15","date_updated":"2026-06-25T08:33:18Z","article_type":"original","publisher":"International Press of Boston","publication_status":"published","status":"public"}]