%0 Journal Article
%T Adequate Closed Form Wave Solutions to the Generalized KdV Equation in Mathematical Physics
%A Md. Munnu Miah
%A Md. Al Amin Meia
%A Md. Matiur Rahman Sarker
%A Ahammodullah Hasan
%J Journal of Applied Mathematics and Physics
%P 2069-2082
%@ 2327-4379
%D 2024
%I Scientific Research Publishing
%R 10.4236/jamp.2024.126126
%X In this paper, we consider the generalized Korteweg-de-Vries (KdV) equations which are remarkable models of the water waves mechanics, the shallow water waves, the quantum mechanics, the ion acoustic waves in plasma, the electro-hydro-dynamical model for local electric field, signal processing waves through optical fibers, etc.<b> </b>We determine the useful and further general exact traveling wave solutions of the above mentioned NLDEs by applying the <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
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  <mi>exp</mi><mrow><mo>(</mo>
   <mrow>
    <mo>&#x2212;</mo><mi>&#x03C4;</mi><mrow><mo>(</mo>
     <mi>&#x03BE;</mi>
    <mo>)</mo></mrow></mrow>
  <mo>)</mo></mrow></mrow>
</math>

-expansion method by aid of traveling wave transformations. Furthermore, we explain the physical significance of the obtained solutions of its definite values of the involved parameters with graphic representations in order to know the physical phenomena. Finally, we show that the <math display='inline' xmlns='http://www.w3.org/1998/Math/MathML'>
 <mrow>
  <mi>exp</mi><mrow><mo>(</mo>
   <mrow>
    <mo>&#x2212;</mo><mi>&#x03C4;</mi><mrow><mo>(</mo>
     <mi>&#x03BE;</mi>
    <mo>)</mo></mrow></mrow>
  <mo>)</mo></mrow></mrow>
</math>

-expansion method is convenient, powerful, straightforward and provide more general solutions and can be helping to examine vast amount of travelling wave solutions to the other different kinds of NLDEs.
%K The Generalized KdV Equation
%K The exp(-<i>&#964
%K </i>(<i>&#958
%K </i>)) -Expansion Method
%K Travelling Wave
%K Solitary Wave
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=133896