New Soliton Solutions for KdV Equations by the Simplest and the Extended Simplest Equation Methods

CSME 2018/08
Volume 39 No.4 : 397-403

New Soliton Solutions for KdV Equations by the Simplest and the Extended Simplest Equation Methods

Sen-Yung Lee^a and Chun-Ku Kuo^b
^aDepartment of Mechanic Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., 701.
^bDepartment of Mechanic Engineering, National Cheng Kung University, Tainan, Taiwan, R.O.C., 701. Department of Mechanical Engineering, Air Force Institute of Technology, Kaohsiung , Taiwan, R.O.C.,820.

Abstract: Four new single-soliton solutions for the Korteweg and de Vries (KdV) equation are developed by the simplest equation method (SEM) with the Bernoulli equation being the simplest equation. These solutions overcome the long existing problem of discontinuity when the nonlinear term coefficient approaches zero and reveal a new phenomenon, named soliton-sliding. In addition, the multi-soliton solutions for the KdV and the potential KdV equations are shown to be obtainable from the SEM by choosing the Burgers equation as the simplest equation. Compared with Hirota’s direct method, the proposed method is more simple and straightforward.

Keywords: KdV, simplest equation method, linearized, soliton-sliding.

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