July 5, 2025 Thesis Open Access

BY LEMESSA REGASSA TOLERA

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<oai_dc:dc xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:oai_dc="http://www.openarchives.org/OAI/2.0/oai_dc/" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd">
  <dc:creator>BY LEMESSA REGASSA TOLERA</dc:creator>
  <dc:date>2025-07-05</dc:date>
  <dc:description>ADVISOR: BOKA KUMSA (PhD)

In this thesis, we presented an analytical approximate solution to the Korteweg–de Vries
(KdV) equation, which has significant applications in various fields such as fluid dynamics,
plasma physics, and nonlinear optics. The kdv equation is solved using Adomian
Decomposition Method (ADM). The main focus of this study is to explore the analytical
approximation of the kdv equation using ADM, which provides rapidly converging series
solutions. The accuracy of this method is demonstrated, and it is shown to be robust for a
variety of boundary and initial conditions. The results suggest that ADM can serve as an
alternative to more complex numerical methods, particularly in cases where exact solutions
are unavailable or difficult to obtain. Furthermore, this thesis refines the ADM is efficient,
convenient, and applicable to a wide range of problems, offering an effective approach for
approximating the solution of the kdv equation.
Keywords: Systems of nonlinear partial differential equations, Adomian decomposition
method, Modified decomposition method and Korteweg de Vries equation (KdV) equation</dc:description>
  <dc:identifier>https://zenodo.org/record/14175</dc:identifier>
  <dc:identifier>10.20372/nadre:14175</dc:identifier>
  <dc:identifier>oai:zenodo.org:14175</dc:identifier>
  <dc:relation>doi:10.20372/nadre:14174</dc:relation>
  <dc:relation>url:https://nadre.ethernet.edu.et/communities/20-25</dc:relation>
  <dc:rights>info:eu-repo/semantics/openAccess</dc:rights>
  <dc:rights>http://www.opensource.org/licenses/opengroup.php</dc:rights>
  <dc:title>ANALYTICAL APPROXIMATE SOLUTION OF KORTEWEG-DE VRIES (KDV) EQUESTION BY ADOMIAN DECOMPOSITION METHOD</dc:title>
  <dc:type>info:eu-repo/semantics/doctoralThesis</dc:type>
  <dc:type>publication-thesis</dc:type>
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