New exact solutions for a generalized variable coefficients 2D KdV equation

2004 ◽  
Vol 19 (5) ◽  
pp. 1083-1086 ◽  
Author(s):  
S.A. Elwakil ◽  
S.K. El-labany ◽  
M.A. Zahran ◽  
R. Sabry
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Variable Coefficients ◽  
New Exact Solutions

scholarly journals AKNS Formalism and Exact Solutions of KdV and Modified KdV Equations with Variable-Coefficients

2016 ◽  
Vol 6 ◽  
pp. 32-41 ◽  
Author(s):  
Supratim Das ◽  
Dibyendu Ghosh
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Elliptic Functions ◽  
Variable Coefficients ◽  
Jacobian Elliptic Functions ◽  
Generalized Kdv Equation ◽  
New Exact Solutions ◽  
Kdv Equations ◽  
Modified Kdv Equation ◽  
Modified Kdv Equations

We apply the AKNS hierarchy to derive the generalized KdV equation andthe generalized modified KdV equation with variable-coefficients. We system-atically derive new exact solutions for them. The solutions turn out to beexpressible in terms of doubly-periodic Jacobian elliptic functions.

New exact solutions of the -dimensional KdV equation with variable coefficients

2005 ◽  
Vol 337 (1-2) ◽  
pp. 101-106 ◽  
Author(s):  
Shoufeng Shen ◽  
Jun Zhang ◽  
Cai'er Ye ◽  
Zuliang Pan
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Variable Coefficients ◽  
New Exact Solutions

A NOTE ON THE EXACT SOLUTION OF THE SPECIAL MODIFIED KdV EQUATION

2008 ◽  
Vol 22 (04) ◽  
pp. 289-293
Author(s):  
HONGLEI WANG ◽  
CHUNHUAN XIANG
Keyword(s):  
Exact Solution ◽  
Exact Solutions ◽  
General Equation ◽  
Vries Equation ◽  
Kdv Equation ◽  
Variable Coefficients ◽  
New Exact Solutions ◽  
Modified Kdv Equation ◽  
De Vries ◽  
Physical Fields

The modified KdV (Korteweg–de Vries) equation with two different variable coefficients can be employed in many different physical fields with time changing. In the present work, by using the truncated expansion, some new exact solutions of the equation are obtained. The general equation may change into lots of other forms KdV equation if we select different parameters.

scholarly journals Exact Solutions for a Third-Order KdV Equation with Variable Coefficients and Forcing Term

2009 ◽  
Vol 2009 ◽  
pp. 1-13 ◽  
Author(s):  
Alvaro H. Salas S ◽  
Cesar A. Gómez S
Keyword(s):  
Exact Solutions ◽  
Periodic Solutions ◽  
Riccati Equation ◽  
Function Method ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Variable Coefficients ◽  
Third Order ◽  
Forcing Term ◽  
Projective Riccati Equation Method

The general projective Riccati equation method and the Exp-function method are used to construct generalized soliton solutions and periodic solutions to special KdV equation with variable coefficients and forcing term.

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