The General Forms of the Multiple-Soliton Solutions for the Completely Integrable Equations by Using the Simplest Equation Method
Applied and Computational Mathematics
Volume 4, Issue 4, August 2015, Pages: 331-334
Received: Jun. 23, 2015;
Accepted: Aug. 6, 2015;
Published: Aug. 14, 2015
Views 3895 Downloads 75
Sen-Yung Lee, Department of Mechanical Engineering, National Cheng Kung University, Taiwan, R.O.C.
Chun-Ku Kuo, Department of Mechanical Engineering, National Cheng Kung University, Taiwan, R.O.C.; Department of Mechanical Engineering, Air Force Institute of Technology, Taiwan, R.O.C.
The simplest equation method with the Burgers’ equation as the simplest equation is used to handle two completely integrable equations, the KdV equation and the potential KdV equation. The general forms of the multiple-soliton solutions are formally established. It is shown that the simplest equation method may provide us with a straightforward and effective mathematic tool for generating multiple-soliton solutions of nonlinear wave equations in fluid mechanics
The General Forms of the Multiple-Soliton Solutions for the Completely Integrable Equations by Using the Simplest Equation Method, Applied and Computational Mathematics.
Vol. 4, No. 4,
2015, pp. 331-334.
Soliman, AA. The modified extended tanh-function method for solving Burgers-type equations. Physica A 361, 394-404 (2006)
Ebaid, A. Exact solitary wave for some nonlinear evolution equations via Exp-function method. Phys. Lett. A 365, 213-219 (2007)
He, JH. Exp-function method for nonlinear wave equations. Chaos Solitons Fractals 30, 700-708 (2006)
Wazwaz, AM. Multipleple-front solutions for the Burgers equation and the coupled Burgers equations. Applied Mathematics and Computation 190, 1198-1206 (2007)
Wazwaz, AM. The tanh method and the sine-cosine methods for a reliable treatment of the modified equal width equation and its variants. Communications in Nonlinear Science and Numerical Simulation 11, 148-160 (2006)
Hirota, R. The direct method in soliton theory. Cambridge, Cambridge University Press 2004.
Hereman, W. Nuseir, A. Symbolic methods to construct exact solutions of nonlinear partial differential equations. Math. Comput. Simulation. 43, 13-27 (1997)
Abdou, MA. The extended F-expansion method and its application for a class of nonlinear evolution equations.Chaos Solitons Fractals 31, 95-104 (2007)
Zayed, EME. Gepreel, KA. The (G_/G)-expansion method for finding traveling wave solutions of nonlinear partial differential equations in mathematical physics. J. Math. Phys. 50, 013502 (2009)
Kudryashov, NA. One method for finding exact solutions of nonlinear differential equations. Commun Nonlinear Sci Numer Simulat 17, 2248-2253 (2012)
Vitanov, NK. On modified method of simplest equation for obtaining exact and approximate solutions of nonlinear PDEs:The role of the simplest equation. Commun Nonlinear Sci Numer Simulat 16, 4215-4231 (2011)
Kudryashov, NA. Seven common errors in finding exact solutions of nonlinear differential equations. Commun. Nonlinear Sci. Numer. Simulat. 14, 3507-3529 (2009)
Vitanov, NK. Application of simplest equations of Bernoulli and Riccati kind for obtaining exact travelling-wave solutions for a class of PDEs with polynominal nonlinearity. Commun Nonlinear Sci Numer Simulat 15, 2050-2060 (2010)
Kudryashov, NA. Modified method of simplest equation:Powerful tool for obtaining exact and approximate travelling-wave solutions of nonlinear PDEs. Commun Nonlinear Sci Numer Simulat 16, 1176-1185 (2011)
Kudryashov, NA. Loguinova, NB. Extended simplest equation method for nonlinear differential equations. Applied Mathematics and Computation 205, 396-402 (2008)
Mohamad, JA. Petkovic, MD. Biswas, A. Modified simple equation method for nonlinear evolution equations. Applied Mathematics and Computation 217, 869-877 (2010)
Peng, G. Wu, X. Wang, LB. Multipleple soliton solutions for the variant Boussinesq equations. Advances in Difference Equations 1, 1-11 (2015)
Wazwaz, AM. Partial differential equations and solitary waves theory. Springer Science & Business Media, 2010.