July 5, 2025 Thesis Open Access

BY LEMESSA REGASSA TOLERA

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  <identifier identifierType="DOI">10.20372/nadre:14175</identifier>
  <creators>
    <creator>
      <creatorName>BY LEMESSA REGASSA TOLERA</creatorName>
    </creator>
  </creators>
  <titles>
    <title>ANALYTICAL APPROXIMATE SOLUTION OF KORTEWEG-DE VRIES (KDV) EQUESTION BY ADOMIAN DECOMPOSITION METHOD</title>
  </titles>
  <publisher>Zenodo</publisher>
  <publicationYear>2025</publicationYear>
  <dates>
    <date dateType="Issued">2025-07-05</date>
  </dates>
  <resourceType resourceTypeGeneral="Text">Thesis</resourceType>
  <alternateIdentifiers>
    <alternateIdentifier alternateIdentifierType="url">https://nadre.ethernet.edu.et/record/14175</alternateIdentifier>
  </alternateIdentifiers>
  <relatedIdentifiers>
    <relatedIdentifier relatedIdentifierType="DOI" relationType="IsVersionOf">10.20372/nadre:14174</relatedIdentifier>
    <relatedIdentifier relatedIdentifierType="URL" relationType="IsPartOf">https://nadre.ethernet.edu.et/communities/20-25</relatedIdentifier>
  </relatedIdentifiers>
  <rightsList>
    <rights rightsURI="http://www.opensource.org/licenses/opengroup.php">Open Group Test Suite License</rights>
    <rights rightsURI="info:eu-repo/semantics/openAccess">Open Access</rights>
  </rightsList>
  <descriptions>
    <description descriptionType="Abstract">&lt;p&gt;ADVISOR: BOKA KUMSA (PhD)&lt;/p&gt;

&lt;p&gt;In this thesis, we presented an analytical approximate solution to the Korteweg&amp;ndash;de Vries&lt;br&gt;
(KdV) equation, which has significant applications in various fields such as fluid dynamics,&lt;br&gt;
plasma physics, and nonlinear optics. The kdv equation is solved using Adomian&lt;br&gt;
Decomposition Method (ADM). The main focus of this study is to explore the analytical&lt;br&gt;
approximation of the kdv equation using ADM, which provides rapidly converging series&lt;br&gt;
solutions. The accuracy of this method is demonstrated, and it is shown to be robust for a&lt;br&gt;
variety of boundary and initial conditions. The results suggest that ADM can serve as an&lt;br&gt;
alternative to more complex numerical methods, particularly in cases where exact solutions&lt;br&gt;
are unavailable or difficult to obtain. Furthermore, this thesis refines the ADM is efficient,&lt;br&gt;
convenient, and applicable to a wide range of problems, offering an effective approach for&lt;br&gt;
approximating the solution of the kdv equation.&lt;br&gt;
Keywords: Systems of nonlinear partial differential equations, Adomian decomposition&lt;br&gt;
method, Modified decomposition method and Korteweg de Vries equation (KdV) equation&lt;/p&gt;</description>
  </descriptions>
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