{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,17]],"date-time":"2026-04-17T03:41:14Z","timestamp":1776397274543,"version":"3.51.2"},"reference-count":41,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2025,12,17]],"date-time":"2025-12-17T00:00:00Z","timestamp":1765929600000},"content-version":"vor","delay-in-days":350,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"},{"start":{"date-parts":[[2025,1,1]],"date-time":"2025-01-01T00:00:00Z","timestamp":1735689600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/doi.wiley.com\/10.1002\/tdm_license_1.1"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2025,1]]},"abstract":"<jats:p>\n                    We investigate the initial value problem associated to the higher order nonlinear Schr\u00f6dinger equation  where\n                    <jats:italic>j<\/jats:italic>\n                    \u2265 2 is any integer,\n                    <jats:italic>u<\/jats:italic>\n                    is a complex valued function, and the initial data\n                    <jats:italic>u<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    is real analytic on\n                    <jats:italic>\u211d<\/jats:italic>\n                    and has a uniform radius of spatial analyticity\n                    <jats:italic>\u03c3<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    in the space variable. For such initial data, we prove that the initial value problem is locally well\u2010posed using space\u2010time estimates and show that the radius of spatial analyticity of the solution remains\n                    <jats:italic>\u03c3<\/jats:italic>\n                    <jats:sub>0<\/jats:sub>\n                    till some lifespan 0 &lt;\n                    <jats:italic>T<\/jats:italic>\n                    \u2264 1. We also show that the uniform radius of spatial analyticity\n                    <jats:italic>\u03c3<\/jats:italic>\n                    (\n                    <jats:italic>t<\/jats:italic>\n                    ) of solutions at time\n                    <jats:italic>t<\/jats:italic>\n                    is bounded from below by  for large time\n                    <jats:italic>t<\/jats:italic>\n                    , where\n                    <jats:italic>c<\/jats:italic>\n                    &gt; 0 is a constant. Our proof relies on standard contraction mapping argument, Plancherel\u2019s Theorem, H\u00f6lder\u2019s inequality, space\u2010time Strichartz estimates for the free Schr\u00f6dinger equation, energy estimate and one\u2010dimensional Sobolev embedding.\n                  <\/jats:p>","DOI":"10.1155\/jama\/9997857","type":"journal-article","created":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T07:28:34Z","timestamp":1766042914000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Algebraic Lower Bounds on the Spatial Analyticity Radius for Higher Order Nonlinear Schr\u00f6dinger Equations"],"prefix":"10.1155","volume":"2025","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4039-3764","authenticated-orcid":false,"given":"Tegegne","family":"Getachew","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3914-3669","authenticated-orcid":false,"given":"Birilew","family":"Belayneh","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0009-0009-6000-9625","authenticated-orcid":false,"given":"Betre","family":"Shiferaw","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2025,12,17]]},"reference":[{"key":"e_1_2_11_1_2","unstructured":"CazenaveT. 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