Modified extended tanh-function method for solving nonlinear partial differential equations

El-Wakil, S.A.; El‐Labany, S. K.; Zahran, M. A.; Sabry, R.

doi:10.1016/s0375-9601(02)00669-2

Cited by 321 publications

(103 citation statements)

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“…The availability of symbolic computations such as Mathematica program has popularized direct seeking for exact solutions of nonlinear equations. Therefore, exact solution methods of nonlinear evolution equations have become more and more important resulting in methods like the tanh method [1][2][3], extended tanh function method [4], the modified extended tanh function method [5], the generalized hyperbolic function [6].Most of exact solutions have been obtained by these methods, including the solitary wave solutions, shock wave solutions, periodic wave solutions, and the like.…”

Section: Introductionmentioning

confidence: 99%

The Tanh Methods for the Hirota Equations

Raslan¹,

Shaeer²

2014

IJCA

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In this paper we applied the tanh method for analytic study of the nonlinear equations of partial differential equations(PDEs).The proposed method gives more general exact traveling wave solutions without much extra effort. Three applications from literature of nonlinear equation of PDEs were solved by the method. The calculations demonstrate the effectiveness and convenience of the method for nonlinear sub system of PDEs.

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Section: Introductionmentioning

confidence: 99%

The Tanh Methods for the Hirota Equations

Raslan¹,

Shaeer²

2014

IJCA

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“…where A i are constants to be determined and the function F (ξ) is defined by the solution of an auxiliary ordinary differential equation(ODE). The exact solutions expressed by a variety of Jacobi elliptic functions (JEFs) of many NLEEs have been obtained by Jacobi elliptic function expansion method (Liu, Fu, Liu, & Zhao, 2001;Chen & Zhang, 2003), mapping method (Peng, 2003;Peng, 2005), F expansion method (Zhao, Wang, & Wang, 2003), extended F expansion method (Abdou, 2007;Liu & Yang, 2004), the generalized Jacobi elliptic function method (Huiqun Zhang, 2007;Chen & Zhang, 2004), and other methods (Elwakil, El-Labany, Zahran, & Sabry, 2002;Khater, Hassan, Krishnan, & Peng, 2008). Various exact solutions were obtained by using these methods, including the solitary wave solutions, shock wave solutions and periodic wave solutions.…”

Section: Introductionmentioning

confidence: 99%

New F Expansion Method and Its Applications to Modified KdV Equation

Bashir¹,

Hakim²

2013

JMR

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In this paper, the new F-expansion method is proposed for constructing more general exact solutions nonlinear evolution equation with the aid of symbolic computation. By using this method, we have successfully obtained some travelling wave solutions of the modified KdV Equation. These exact solutions include the hyperbolic function solutions, trigonometric function solutions, rational function solutions and Jacobi elliptic function solutions. Also it is shown that the proposed method is efficient for solving nonlinear evolution equations in mathematical physics and in engineering.

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“…The tanh-function method is the well known method as a direct selection of the function F(ξ)=tanh( ξ). Recently, many exact solutions expressed by various Jacobi elliptic functions (JEFs) of many NLEEs have been obtained by Jacobi elliptic function expansion method [7][8][9][10], mapping method [11,12], F-expansion method [13], extended F-expansion method [14], the generalized Jacobi elliptic function method [15] and other methods [16][17][18][19][20]. Various exact solutions were obtained by using these methods, including the solitary wave solutions, shock wave solutions and periodic wave solutions.…”

Section: Introductionmentioning

confidence: 99%