The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method
Applied and Computational Mathematics
Volume 4, Issue 5, October 2015, Pages: 335-341
Received: Jun. 29, 2015; Accepted: Aug. 5, 2015; Published: Aug. 19, 2015
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Authors
Sen-Yung Lee, Department of Mechanical Engineering, National Cheng Kung University, Taiwan, R.O.C.
Chun-Ku Kuo, Department of Mechanical Engineering, Air Force Institute of Technology, Taiwan, R.O.C.
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Abstract
The general form of linearized exact solution for the Korteweg and de Vries (KdV) equation, with an arbitrary nonlinear coefficient, is derived by the simplest equation method with the Bernoulli equation as the simplest equation. It is shown that the proposed exact solution overcomes the long existing problem of discontinuity and can be successfully reduced to linearity, while the nonlinear term coefficient approaches zero. Comparison of four different soliton solutions is presented. A new phenomenon, named soliton sliding, is observed.
Keywords
General Form, Linearized, KdV, Simplest Equation Method, Bernoulli, Discontinuity, Soliton Sliding
To cite this article
Sen-Yung Lee, Chun-Ku Kuo, The General Form of Linearized Exact Solution for the KdV Equation by the Simplest Equation Method, Applied and Computational Mathematics. Vol. 4, No. 5, 2015, pp. 335-341. doi: 10.11648/j.acm.20150405.11
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