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Explicit analytic solution for the nonlinear ion sound waves equation

Doosthoseini, A ; Sharif University of Technology | 2010

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  1. Type of Document: Article
  2. Publisher: 2010
  3. Abstract:
  4. In this article, we use an efficient analytical method called homotopy analysis method (HAM) to derive an approximate solution of nonlinear ion sound waves equation. Actually, we solved Korteweg-de Vries equation arises in a one-dimensional macroscopic plasma model describing the weakly nonlinear evolution of ion sound speed by the HAM. Unlike the perturbation method, the HAM does not require the addition of a small physically parameter to the differential equation. It is applica-ble to strongly and weakly nonlinear problems. Moreover, the HAM involves an auxiliary parameter, which renders the convergence param-eter of series solutions controllable, and increases the convergence, and increases the convergence signi cantly. This article depicts that the HAM is an efficient and powerful method for solving nonlinear differential equations. Its performance is considerable and the solution of the equation is the same as the numerical methods solution
  5. Keywords:
  6. Homotopy analysis method ; Korteweg-de Vries equation ; Nonlinear ion sound waves equation ; Plasma physics
  7. Source: Applied Mathematical Sciences ; Volume 4, Issue 21-24 , 2010 , Pages 1183-1195 ; 1312885X (ISSN)