{"abstracts":[{"sha1":"0567dd2b1b22b3bf3475af36df9678ce94968676","content":"Abstract\n\t The singularly perturbed Riccati equation is the first-order nonlinear ordinary differential equation \n\t \n\t\t\n\t\t\n$\\hbar \\partial _x f = af^2 + bf + c$\n\n\t \n\t in the complex domain where \n\t \n\t\t\n\t\t\n$\\hbar $\n\n\t \n\t is a small complex parameter. We prove an existence and uniqueness theorem for exact solutions with prescribed asymptotics as \n\t \n\t\t\n\t\t\n$\\hbar \\to 0$\n\n\t \n\t in a half-plane. These exact solutions are constructed using the Borel–Laplace method; that is, they are Borel summations of the formal divergent \n\t \n\t\t\n\t\t\n$\\hbar $\n\n\t \n\t -power series solutions. As an application, we prove existence and uniqueness of exact WKB solutions for the complex one-dimensional Schrödinger equation with a rational potential.","mimetype":"application/xml+jats"}],"refs":[{"index":0,"extra":{"doi":"10.1007/s00023-013-0239-7"},"key":"S0027763022000381_r5"},{"index":1,"extra":{"doi":"10.1007/s10240-014-0066-5"},"key":"S0027763022000381_r2"},{"index":2,"extra":{"authors":["Dunster"],"doi":"10.1098/rspa.1993.0003","volume":"440"},"key":"S0027763022000381_r4","year":1993,"container_name":"Proc. Roy. Soc. Lond. Ser. A","title":"Convergent Liouville–Green expansions for second-order linear differential equations, with an application to Bessel functions","locator":"37"},{"index":3,"extra":{"unstructured":"[13] Nikolaev, N. , Triangularisation of singularly perturbed logarithmic differential systems of rank 2, preprint, arXiv:1909.04011"},"key":"S0027763022000381_r13"},{"index":4,"extra":{"authors":["Aoki"],"volume-title":"ICM-90 Satellite Conference Proceedings: Special Functions"},"key":"S0027763022000381_r1","year":1991,"container_name":"ICM-90 Satellite Conference Proceedings: Special Functions"},{"index":5,"extra":{"authors":["Reid"],"volume-title":"Riccati Differential Equations"},"key":"S0027763022000381_r15","year":1972,"container_name":"Riccati Differential Equations"},{"index":6,"extra":{"doi":"10.1007/978-3-662-02414-0"},"key":"S0027763022000381_r18"},{"index":7,"extra":{"doi":"10.1090/mmono/227"},"key":"S0027763022000381_r8"},{"index":8,"extra":{"doi":"10.1007/978-3-319-29075-1"},"key":"S0027763022000381_r9"},{"index":9,"extra":{"doi":"10.1201/9781439864548"},"key":"S0027763022000381_r14"},{"index":10,"extra":{"unstructured":"[12] Nikolaev, N. , Existence and uniqueness of exact WKB solutions for second-order linear ODEs, to appear in Commun. Math. Phys., preprint, arXiv:2106.10248"},"key":"S0027763022000381_r12"},{"index":11,"extra":{"doi":"10.1063/1.524408"},"key":"S0027763022000381_r17"},{"index":12,"extra":{"authors":["Wasow"],"volume-title":"Asymptotic Expansions for Ordinary Differential Equations"},"key":"S0027763022000381_r21","year":1976,"container_name":"Asymptotic Expansions for Ordinary Differential Equations"},{"index":13,"extra":{"authors":["Delabaere"],"doi":"10.5802/aif.1326","volume":"43"},"key":"S0027763022000381_r3","year":1993,"container_name":"Ann. Inst. Fourier (Grenoble)","title":"Résurgence de voros et périodes des courbes hyperelliptiques","locator":"163"},{"index":14,"extra":{"doi":"10.1103/physrevlett.55.2523"},"key":"S0027763022000381_r16"},{"index":15,"extra":{"doi":"10.1007/978-3-319-52842-7_5"},"key":"S0027763022000381_r19"},{"index":16,"extra":{"doi":"10.1088/1751-8113/47/47/474009"},"key":"S0027763022000381_r7"},{"index":17,"extra":{"doi":"10.1016/j.aim.2012.09.027"},"key":"S0027763022000381_r6"},{"index":18,"extra":{"doi":"10.1016/j.jat.2021.105562"},"key":"S0027763022000381_r10"},{"index":19,"extra":{"doi":"10.1007/s00029-021-00688-5"},"key":"S0027763022000381_r11"},{"index":20,"extra":{"authors":["Voros"],"volume":"39"},"key":"S0027763022000381_r20","year":1983,"container_name":"Ann. Inst. Henri Poincaré Phys. Théor.","title":"The return of the quartic oscillator. The complex WKB method","locator":"211"}],"contribs":[{"index":0,"creator_id":"adovx2lpcbbhhhfv27cpwxge7m","creator":{"orcid":"0000-0002-7042-0479","surname":"Nikolaev","given_name":"Nikita","display_name":"Nikita Nikolaev","state":"active","ident":"adovx2lpcbbhhhfv27cpwxge7m","revision":"6fc90e43-07c8-430c-bece-687663dc7a3b"},"raw_name":"NIKITA NIKOLAEV","given_name":"NIKITA","surname":"NIKOLAEV","role":"author","extra":{"seq":"first"}}],"license_slug":"CC-BY","language":"en","publisher":"Cambridge University Press (CUP)","pages":"1-36","ext_ids":{"doi":"10.1017/nmj.2022.38"},"release_year":2022,"release_date":"2022-12-08","release_stage":"published","release_type":"article-journal","container_id":"354b2ocplvgx5caiktzsvnk7iy","webcaptures":[],"filesets":[],"files":[{"release_ids":["2ne52ynm55hcfdti3sxi2gne3m"],"mimetype":"application/pdf","urls":[{"url":"https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B0BF61AD5757208DA77AE7308664D0EE/S0027763022000381a.pdf/div-class-title-exact-solutions-for-the-singularly-perturbed-riccati-equation-and-exact-wkb-analysis-div.pdf","rel":"publisher"},{"url":"https://web.archive.org/web/20221211012717/https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B0BF61AD5757208DA77AE7308664D0EE/S0027763022000381a.pdf/div-class-title-exact-solutions-for-the-singularly-perturbed-riccati-equation-and-exact-wkb-analysis-div.pdf","rel":"webarchive"}],"sha256":"6409ad82c09d56342ef1483eabbb2fb84b821cedb920caf058acee87640c2a3c","sha1":"c678499a8cb5cca6bc59aea4d8feff73f89701a6","md5":"b854774cb520852473ddeef63031f246","size":1017560,"revision":"5aadc3af-33ff-4ad7-acdf-92c699937c08","ident":"guimms6dmbcozfgub6gb2jyiw4","state":"active"}],"container":{"wikidata_qid":"Q15490097","issnp":"0027-7630","issne":"2152-6842","issnl":"0027-7630","publisher":"Cambridge University Press","name":"Nagoya mathematical journal","extra":{"country":"uk","ezb":{"color":"red","ezb_id":"133423"},"kbart":{"clockss":{"year_spans":[[2017,2022]]},"hathitrust":{"year_spans":[]},"portico":{"year_spans":[[1950,2022]]}},"publisher_type":"unipress","sherpa_romeo":{"color":"green"},"szczepanski":{"as_of":"2018"},"urls":["https://www.cambridge.org/core/journals/nagoya-mathematical-journal","http://projecteuclid.org/Dienst/UI/1.0/Journal?authority=euclid.nmj","http://projecteuclid.org/nmj"]},"revision":"b562bc6a-2763-4f09-bf7d-52fabb264612","ident":"354b2ocplvgx5caiktzsvnk7iy","state":"active"},"work_id":"j4sygmtifrfrpjmqnrhvez4nzi","title":"EXACT SOLUTIONS FOR THE SINGULARLY PERTURBED RICCATI EQUATION AND EXACT WKB ANALYSIS","state":"active","ident":"2ne52ynm55hcfdti3sxi2gne3m","revision":"0c44abaf-54b6-4004-a676-3e90ef809e8a","extra":{"crossref":{"alternative-id":["S0027763022000381"],"license":[{"URL":"https://creativecommons.org/licenses/by/4.0/","content-version":"unspecified","delay-in-days":0,"start":"2022-12-08T00:00:00Z"}],"subject":["General Mathematics"],"type":"journal-article"}}}