<?xml version="1.0" encoding="utf-8"?>
<TEI xmlns="http://www.tei-c.org/ns/1.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:hal="http://hal.archives-ouvertes.fr/" xmlns:gml="http://www.opengis.net/gml/3.3/" xmlns:gmlce="http://www.opengis.net/gml/3.3/ce" version="1.1" xsi:schemaLocation="http://www.tei-c.org/ns/1.0 http://api.archives-ouvertes.fr/documents/aofr-sword.xsd">
  <teiHeader>
    <fileDesc>
      <titleStmt>
        <title>HAL TEI export of hal-04677959v3</title>
      </titleStmt>
      <publicationStmt>
        <distributor>CCSD</distributor>
        <availability status="restricted">
          <licence target="https://creativecommons.org/publicdomain/zero/1.0/">CC0 1.0 - Universal</licence>
        </availability>
        <date when="2026-05-15T18:37:07+02:00"/>
      </publicationStmt>
      <sourceDesc>
        <p part="N">HAL API Platform</p>
      </sourceDesc>
    </fileDesc>
  </teiHeader>
  <text>
    <body>
      <listBibl>
        <biblFull>
          <titleStmt>
            <title xml:lang="en">Time  splitting and error estimates for nonlinear  Schrodinger equations  with a potential</title>
            <author role="aut">
              <persName>
                <forename type="first">Rémi</forename>
                <surname>Carles</surname>
              </persName>
              <email type="md5">24f57f46a11054c84e660da75dcadef3</email>
              <email type="domain">math.cnrs.fr</email>
              <ptr type="url" target="https://carles.perso.math.cnrs.fr/"/>
              <idno type="idhal" notation="string">remicarles</idno>
              <idno type="idhal" notation="numeric">886</idno>
              <idno type="halauthorid" notation="string">21695-886</idno>
              <idno type="ORCID">https://orcid.org/0000-0002-8866-587X</idno>
              <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=2u9hq5gAAAAJ&amp;hl=fr&amp;oi=sra</idno>
              <idno type="IDREF">https://www.idref.fr/12889704X</idno>
              <affiliation ref="#struct-1096399"/>
            </author>
            <editor role="depositor">
              <persName>
                <forename>Rémi</forename>
                <surname>Carles</surname>
              </persName>
              <email type="md5">24f57f46a11054c84e660da75dcadef3</email>
              <email type="domain">math.cnrs.fr</email>
            </editor>
            <funder ref="#projanr-38048"/>
          </titleStmt>
          <editionStmt>
            <edition n="v1">
              <date type="whenSubmitted">2024-08-26 15:44:35</date>
            </edition>
            <edition n="v2">
              <date type="whenSubmitted">2024-08-30 10:43:57</date>
            </edition>
            <edition n="v3" type="current">
              <date type="whenSubmitted">2025-07-15 10:53:52</date>
              <date type="whenModified">2025-07-23 03:13:03</date>
              <date type="whenReleased">2025-07-21 11:29:48</date>
              <date type="whenProduced">2025-07-15</date>
              <date type="whenEndEmbargoed">2025-07-15</date>
              <ref type="file" target="https://hal.science/hal-04677959v3/document">
                <date notBefore="2025-07-15"/>
              </ref>
              <ref type="file" subtype="author" n="1" target="https://hal.science/hal-04677959v3/file/split-potential-final.pdf" id="file-5162456-4454938">
                <date notBefore="2025-07-15"/>
              </ref>
              <ref type="externalLink" target="http://arxiv.org/pdf/2408.14816"/>
            </edition>
            <respStmt>
              <resp>contributor</resp>
              <name key="102497">
                <persName>
                  <forename>Rémi</forename>
                  <surname>Carles</surname>
                </persName>
                <email type="md5">24f57f46a11054c84e660da75dcadef3</email>
                <email type="domain">math.cnrs.fr</email>
              </name>
            </respStmt>
          </editionStmt>
          <publicationStmt>
            <distributor>CCSD</distributor>
            <idno type="halId">hal-04677959</idno>
            <idno type="halUri">https://hal.science/hal-04677959</idno>
            <idno type="halBibtex">carles:hal-04677959</idno>
            <idno type="halRefHtml">2025</idno>
            <idno type="halRef">2025</idno>
            <availability status="restricted">
              <licence target="https://creativecommons.org/licenses/by/4.0/">CC BY 4.0 - Attribution<ref corresp="#file-5162456-4454938"/></licence>
            </availability>
          </publicationStmt>
          <seriesStmt>
            <idno type="stamp" n="UNIV-RENNES1">Université de Rennes 1</idno>
            <idno type="stamp" n="IRMAR">Institut de Recherche Mathématique de Rennes</idno>
            <idno type="stamp" n="UR2-HB">Université Rennes 2 - Haute Bretagne</idno>
            <idno type="stamp" n="CNRS">CNRS - Centre national de la recherche scientifique</idno>
            <idno type="stamp" n="INSA-RENNES">Institut National des Sciences Appliquées de Rennes</idno>
            <idno type="stamp" n="INSMI">CNRS-INSMI - INstitut des Sciences Mathématiques et de leurs Interactions</idno>
            <idno type="stamp" n="IRMAR-EDP" corresp="IRMAR">Equations aux dérivées partielles</idno>
            <idno type="stamp" n="CHL">Centre Henri Lebesgue</idno>
            <idno type="stamp" n="TDS-MACS">Réseau de recherche en Théorie des Systèmes Distribués, Modélisation, Analyse et Contrôle des Systèmes</idno>
            <idno type="stamp" n="UR1-HAL">Publications labos UR1 dans HAL-Rennes 1</idno>
            <idno type="stamp" n="UR1-MATH-STIC">UR1 - publications Maths-STIC</idno>
            <idno type="stamp" n="UNIV-RENNES2">Université Rennes 2</idno>
            <idno type="stamp" n="TEST-UR-CSS">TEST Université de Rennes CSS</idno>
            <idno type="stamp" n="UNIV-RENNES">Université de Rennes</idno>
            <idno type="stamp" n="INSA-GROUPE">Groupe INSA</idno>
            <idno type="stamp" n="ANR">ANR</idno>
            <idno type="stamp" n="UR1-MATH-NUM">Pôle UnivRennes - Mathématiques - Numérique </idno>
            <idno type="stamp" n="INSTITUT-AGRO">Institut Agro</idno>
          </seriesStmt>
          <notesStmt>
            <note type="commentary">More comments and explanations in the introduction.</note>
          </notesStmt>
          <sourceDesc>
            <biblStruct>
              <analytic>
                <title xml:lang="en">Time  splitting and error estimates for nonlinear  Schrodinger equations  with a potential</title>
                <author role="aut">
                  <persName>
                    <forename type="first">Rémi</forename>
                    <surname>Carles</surname>
                  </persName>
                  <email type="md5">24f57f46a11054c84e660da75dcadef3</email>
                  <email type="domain">math.cnrs.fr</email>
                  <ptr type="url" target="https://carles.perso.math.cnrs.fr/"/>
                  <idno type="idhal" notation="string">remicarles</idno>
                  <idno type="idhal" notation="numeric">886</idno>
                  <idno type="halauthorid" notation="string">21695-886</idno>
                  <idno type="ORCID">https://orcid.org/0000-0002-8866-587X</idno>
                  <idno type="GOOGLE SCHOLAR">https://scholar.google.fr/citations?user=2u9hq5gAAAAJ&amp;hl=fr&amp;oi=sra</idno>
                  <idno type="IDREF">https://www.idref.fr/12889704X</idno>
                  <affiliation ref="#struct-1096399"/>
                </author>
              </analytic>
              <monogr>
                <imprint/>
              </monogr>
              <idno type="arxiv">2408.14816</idno>
            </biblStruct>
          </sourceDesc>
          <profileDesc>
            <langUsage>
              <language ident="en">English</language>
            </langUsage>
            <textClass>
              <classCode scheme="halDomain" n="math.math-na">Mathematics [math]/Numerical Analysis [math.NA]</classCode>
              <classCode scheme="halDomain" n="math.math-ap">Mathematics [math]/Analysis of PDEs [math.AP]</classCode>
              <classCode scheme="halDomain" n="math.math-mp">Mathematics [math]/Mathematical Physics [math-ph]</classCode>
              <classCode scheme="halTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halOldTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
              <classCode scheme="halTreeTypology" n="UNDEFINED">Preprints, Working Papers, ...</classCode>
            </textClass>
            <abstract xml:lang="en">
              <p>We consider the nonlinear Schrödinger equation with a potential, also known as Gross-Pitaevskii equation. By introducing a suitable spectral localization, we prove low regularity error estimates for the time discretization corresponding to an adapted Lie-Trotter splitting scheme. The proof is based on tools from spectral theory and pseudodifferential calculus in order to obtain various estimates on the spectral localization, including discrete Strichartz estimates which support the nonlinear analysis.</p>
            </abstract>
          </profileDesc>
        </biblFull>
      </listBibl>
    </body>
    <back>
      <listOrg type="structures">
        <org type="laboratory" xml:id="struct-1096399" status="VALID">
          <idno type="IdRef">028233107</idno>
          <idno type="RNSR">199612396W</idno>
          <idno type="ROR">https://ror.org/05y76vp22</idno>
          <orgName>Institut de Recherche Mathématique de Rennes</orgName>
          <orgName type="acronym">IRMAR</orgName>
          <date type="start">2022-01-01</date>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, bâtiments 22 et 23, 263 avenue du Général Leclerc, CS 7420535042  RENNES Cédex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://irmar.univ-rennes1.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-105160" type="direct"/>
            <relation active="#struct-117606" type="direct"/>
            <relation active="#struct-301232" type="indirect"/>
            <relation active="#struct-247362" type="direct"/>
            <relation active="#struct-406201" type="direct"/>
            <relation name="UMR6625" active="#struct-441569" type="direct"/>
            <relation active="#struct-1091012" type="direct"/>
            <relation active="#struct-1042499" type="indirect"/>
          </listRelation>
        </org>
        <org type="institution" xml:id="struct-105160" status="VALID">
          <idno type="IdRef">26693823X</idno>
          <idno type="ROR">https://ror.org/015m7wh34</idno>
          <orgName>Université de Rennes</orgName>
          <orgName type="acronym">UR</orgName>
          <desc>
            <address>
              <addrLine>Campus de Beaulieu, 263 avenue Général Leclerc, CS 74205, 35042 RENNES CEDEX</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.univ-rennes.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-117606" status="VALID">
          <idno type="ROR">https://ror.org/04xaa4j22</idno>
          <orgName>Institut National des Sciences Appliquées - Rennes</orgName>
          <orgName type="acronym">INSA Rennes</orgName>
          <desc>
            <address>
              <addrLine>20, avenue des Buttes de Coësmes - CS 70839 - 35708 Rennes cedex 7</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.insa-rennes.fr/</ref>
          </desc>
          <listRelation>
            <relation active="#struct-301232" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-301232" status="VALID">
          <idno type="IdRef">162105150</idno>
          <orgName>Institut National des Sciences Appliquées</orgName>
          <orgName type="acronym">INSA</orgName>
          <desc>
            <address>
              <country key="FR"/>
            </address>
          </desc>
        </org>
        <org type="institution" xml:id="struct-247362" status="VALID">
          <idno type="ROR">https://ror.org/03rxtdc22</idno>
          <orgName>École normale supérieure - Rennes</orgName>
          <orgName type="acronym">ENS Rennes</orgName>
          <desc>
            <address>
              <addrLine>Campus de Ker Lann - avenue Robert Schuman - 35170 Bruz</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.ens-rennes.fr</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-406201" status="VALID">
          <idno type="IdRef">054447658</idno>
          <idno type="ISNI">0000000121522279</idno>
          <idno type="ROR">https://ror.org/01m84wm78</idno>
          <orgName>Université de Rennes 2</orgName>
          <orgName type="acronym">UR2</orgName>
          <desc>
            <address>
              <addrLine>Place du recteur Henri Le Moal - CS 24307 - 35043 Rennes cedex</addrLine>
              <country key="FR"/>
            </address>
            <ref type="url">http://www.univ-rennes2.fr/</ref>
          </desc>
        </org>
        <org type="regroupinstitution" xml:id="struct-441569" status="VALID">
          <idno type="IdRef">02636817X</idno>
          <idno type="ISNI">0000000122597504</idno>
          <idno type="ROR">https://ror.org/02feahw73</idno>
          <orgName>Centre National de la Recherche Scientifique</orgName>
          <orgName type="acronym">CNRS</orgName>
          <date type="start">1939-10-19</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.cnrs.fr/</ref>
          </desc>
        </org>
        <org type="institution" xml:id="struct-1091012" status="VALID">
          <idno type="IdRef">261039946</idno>
          <idno type="ROR">https://ror.org/01s3fs709</idno>
          <orgName>Institut Agro Rennes Angers</orgName>
          <date type="start">2022-01-01</date>
          <desc>
            <address>
              <addrLine>65 rue de Saint Brieuc CS 84215 35042 Rennes CEDEX</addrLine>
              <country key="FR"/>
            </address>
          </desc>
          <listRelation>
            <relation active="#struct-1042499" type="direct"/>
          </listRelation>
        </org>
        <org type="regroupinstitution" xml:id="struct-1042499" status="VALID">
          <idno type="IdRef">260373249</idno>
          <idno type="ROR">https://ror.org/01dkyve95</idno>
          <orgName>Institut national d'enseignement supérieur pour l'agriculture, l'alimentation et l'environnement</orgName>
          <orgName type="acronym">Institut Agro</orgName>
          <date type="start">2020-01-01</date>
          <desc>
            <address>
              <country key="FR"/>
            </address>
            <ref type="url">https://www.institut-agro.fr</ref>
          </desc>
        </org>
      </listOrg>
      <listOrg type="projects">
        <org type="anrProject" xml:id="projanr-38048" status="VALID">
          <idno type="anr">ANR-11-LABX-0020</idno>
          <idno type="program">Laboratoires d'excellence</idno>
          <orgName>LEBESGUE</orgName>
          <desc>Centre de Mathématiques Henri Lebesgue : fondements, interactions, applications et Formation</desc>
          <date type="start">2011</date>
        </org>
      </listOrg>
    </back>
  </text>
</TEI>