<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>0120-419X</journal-id>
<journal-title><![CDATA[Revista Integración]]></journal-title>
<abbrev-journal-title><![CDATA[Integración - UIS]]></abbrev-journal-title>
<issn>0120-419X</issn>
<publisher>
<publisher-name><![CDATA[Universidad Industrial de Santander]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S0120-419X2021000200257</article-id>
<article-id pub-id-type="doi">10.18273/revint.v39n2-2021007</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Optimal system, invariant solutions and complete classification of Lie group symmetries for a generalized Kummer-Schwarz equation and its Lie algebra representation]]></article-title>
<article-title xml:lang="es"><![CDATA[Sistema óptimo, soluciones invariantes y clasificación completa del grupo de simetrías de Lie para la ecuación de Kummer-Schwarz generalizada y su representación del álgebra de Lie]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[GARCÍA HERNÁNDEZ]]></surname>
<given-names><![CDATA[DANILO A.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[DUQUE]]></surname>
<given-names><![CDATA[O. M. L.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[ACEVEDO]]></surname>
<given-names><![CDATA[Y.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[LOAIZA]]></surname>
<given-names><![CDATA[G.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,IMEC-UNICAMP  ]]></institution>
<addr-line><![CDATA[Campinas ]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,IMEC-UNICAMP  ]]></institution>
<addr-line><![CDATA[Campinas ]]></addr-line>
<country>Brazil</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,Universidad EAFIT Departamento de ciencias matemáticas ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<aff id="Af4">
<institution><![CDATA[,Universidad EAFIT Departamento de ciencias matemáticas ]]></institution>
<addr-line><![CDATA[Medellín ]]></addr-line>
<country>Colombia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>39</volume>
<numero>2</numero>
<fpage>257</fpage>
<lpage>274</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_arttext&amp;pid=S0120-419X2021000200257&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_abstract&amp;pid=S0120-419X2021000200257&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.co/scielo.php?script=sci_pdf&amp;pid=S0120-419X2021000200257&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract. We obtain the complete classification of the Lie symmetry group and the optimal system's generating operators associated with a particular case of the generalized Kummer - Schwarz equation. Using those operators we characterize all invariant solutions, alternative solutions were found for the equation studied and the Lie algebra associated with the symmetry group is classified. MSC2010: 35A30, 58J70, 76M60.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Resumen. Obtenemos la clasificación completa del grupo de simetría de Lie y los operadores generadores del sistema optimal asociados a un caso particular de la ecuación de Kummer - Schwarz generalizada. Utilizando esos operadores, caracterizamos todas las soluciones invariantes, se encontraron soluciones alternativas para la ecuación estudiada y se clasifica el álgebra de Lie asociada al grupo de simetría.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Invariant solutions]]></kwd>
<kwd lng="en"><![CDATA[Lie symmetry group]]></kwd>
<kwd lng="en"><![CDATA[Optimal system]]></kwd>
<kwd lng="en"><![CDATA[Lie algebra classification]]></kwd>
<kwd lng="en"><![CDATA[Kummer-Schwarz equation]]></kwd>
<kwd lng="es"><![CDATA[Soluciones invariantes]]></kwd>
<kwd lng="es"><![CDATA[grupo de simetría de Lie]]></kwd>
<kwd lng="es"><![CDATA[Sistema optimal]]></kwd>
<kwd lng="es"><![CDATA[Clasificación del álgebra de Lie]]></kwd>
<kwd lng="es"><![CDATA[Ecuación de Kummer - Schwarz]]></kwd>
</kwd-group>
</article-meta>
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