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  <doc>
    <id>1317</id>
    <completedYear/>
    <publishedYear/>
    <thesisYearAccepted/>
    <language>eng</language>
    <pageFirst/>
    <pageLast/>
    <pageNumber/>
    <edition/>
    <issue/>
    <volume/>
    <type>reportzib</type>
    <publisherName/>
    <publisherPlace/>
    <creatingCorporation/>
    <contributingCorporation/>
    <belongsToBibliography>0</belongsToBibliography>
    <completedDate>2011-06-21</completedDate>
    <publishedDate>2011-06-21</publishedDate>
    <thesisDateAccepted>--</thesisDateAccepted>
    <title language="eng">Exact solutions of nonlinear partial differential equations   by the method of group foliation reduction</title>
    <abstract language="eng">A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in multi-dimensions. &#13;
&#13;
The method is based on group foliation reduction&#13;
and employs a separation ansatz to solve &#13;
an equivalent first-order group foliation system &#13;
whose independent and dependent variables &#13;
respectively consist of the invariants and differential invariants of a given one-dimensional group of point symmetries&#13;
for the reaction-diffusion equation. &#13;
&#13;
With this method, solutions of the reaction-diffusion equation &#13;
&#13;
are obtained in an explicit form, including &#13;
&#13;
group-invariant similarity solutions and travelling-wave solutions, &#13;
&#13;
as well as dynamically interesting solutions that are not invariant under&#13;
&#13;
any of the point symmetries admitted by this equation.</abstract>
    <identifier type="serial">11-25</identifier>
    <identifier type="urn">urn:nbn:de:0297-zib-13171</identifier>
    <enrichment key="SourceTitle">Appeared in: SIGMA 7 (2011), 066, 10 pages.</enrichment>
    <author>Stephen Anco</author>
    <submitter>Winfried Neun</submitter>
    <author>Sajid Ali</author>
    <author>Thomas Wolf</author>
    <series>
      <title>ZIB-Report</title>
      <number>11-25</number>
    </series>
    <subject>
      <language>deu</language>
      <type>uncontrolled</type>
      <value>semilinear heat equation, similarity reduction, exact solutions,  group foliation, symmetry</value>
    </subject>
    <collection role="msc" number="34-XX">ORDINARY DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="35-XX">PARTIAL DIFFERENTIAL EQUATIONS</collection>
    <collection role="msc" number="58-XX">GLOBAL ANALYSIS, ANALYSIS ON MANIFOLDS [See also 32Cxx, 32Fxx, 32Wxx, 46-XX, 47Hxx, 53Cxx](For geometric integration theory, see 49Q15)</collection>
    <collection role="institutes" number="sis">Digital Data and Information for Society, Science, and Culture</collection>
    <file>https://opus4.kobv.de/opus4-zib/files/1317/ZR-11-25.ps</file>
    <file>https://opus4.kobv.de/opus4-zib/files/1317/ZR-11-25.pdf</file>
  </doc>
</export-example>
