An automated tanh-function method for finding solitary wave solutions to non-linear evolution equations

1996 ◽  
Vol 98 (3) ◽  
pp. 288-300 ◽  
Author(s):  
E.J. Parkes ◽  
B.R. Duffy
Keyword(s):  
Solitary Wave ◽  
Function Method ◽  
Evolution Equations ◽  
Solitary Wave Solutions ◽  
Linear Evolution ◽  
Wave Solutions ◽  
Non Linear ◽  
Linear Evolution Equations

scholarly journals Multi-wave solutions for a non-isospectral KDV-type equation with variable coefficients

2012 ◽  
Vol 16 (5) ◽  
pp. 1476-1479 ◽  
Author(s):  
Sheng Zhang ◽  
Qun Gao ◽  
Qian-An Zong ◽  
Dong Liu
Keyword(s):  
Variable Coefficient ◽  
Function Method ◽  
Evolution Equations ◽  
Vries Equation ◽  
Type Equation ◽  
Variable Coefficients ◽  
Linear Evolution ◽  
Wave Solutions ◽  
De Vries ◽  
Linear Evolution Equations

As a typical mathematical model in fluids and plasmas, Korteweg-de Vries equation is famous. In this paper, the Exp-function method is extended to a nonisos-pectral Korteweg-de Vries type equation with three variable coefficients, and multi-wave solutions are obtained. It is shown that the Expfunction method combined with appropriate ansatz may provide with a straightforward, effective and alternative method for constructing multi-wave solutions of variable-coefficient non-linear evolution equations.

scholarly journals A direct algorithm of exp-function method for non-linear evolution equations in fluids

2016 ◽  
Vol 20 (3) ◽  
pp. 881-884 ◽  
Author(s):  
Sheng Zhang ◽  
Jiahong Li ◽  
Luyao Zhang
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Evolution Equations ◽  
Mathematical Tool ◽  
Direct Algorithm ◽  
Linear Evolution ◽  
Non Linear ◽  
De Vries ◽  
Linear Evolution Equations

In this paper, a direct algorithm of the exp-function method is proposed for exactly solving non-linear evolution equations. To illustrate the validity and advantages of the algorithm, the Korteweg-de Vries and Jimbo-Miwa equations are considered. As a result, exact solutions are obtained. It is shown that the exp-function method with the direct algorithm provides a simpler but effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids.

scholarly journals Simplest exp-function method for exact solutions of Mikhauilov-Novikov-Wang equations

2019 ◽  
Vol 23 (4) ◽  
pp. 2381-2388 ◽  
Author(s):  
Sheng Zhang ◽  
Caihong You ◽  
Bo Xu
Keyword(s):  
Exact Solutions ◽  
Function Method ◽  
Evolution Equations ◽  
Mathematical Tool ◽  
Direct Algorithm ◽  
Linear Evolution ◽  
Non Linear ◽  
Linear Evolution Equations

In this paper, the simplest exp-function method which combines the exp-function method with a direct algorithm is used to exactly solve the Mikhauilov-Novikov-Wang equations. As a result, two explicit and exact solutions are obtained. It is shown that the simplest exp-function method provides a simpler but more effective mathematical tool for constructing exact solutions of non-linear evolution equations in fluids.

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