scholarly journals New Exact Solutions of a Generalized KdV Equation with Variable Coefficients

2013 ◽  
Vol 02 (01) ◽  
pp. 42-47
Author(s):  
佳梅 张
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Variable Coefficients ◽  
Generalized Kdv Equation ◽  
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 for a generalized KdV equation

2018 ◽  
Vol 92 (2) ◽  
pp. 215-219 ◽  
Author(s):  
Lingfei Li ◽  
Yingying Xie ◽  
Shihui Zhu
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Generalized Kdv Equation ◽  
New Exact Solutions

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.

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

New exact solutions to the generalized KdV equation with generalized evolution

Pramana ◽  
2012 ◽  
Vol 78 (4) ◽  
pp. 499-511 ◽  
Author(s):  
YONGAN XIE ◽  
SHENGQIANG TANG ◽  
DAHE FENG
Keyword(s):  
Exact Solutions ◽  
Kdv Equation ◽  
Generalized Kdv Equation ◽  
New Exact Solutions

SOLVING THE GENERALIZED BURGERS–KdV EQUATION BY A COMBINATION METHOD

2008 ◽  
Vol 22 (21) ◽  
pp. 2021-2025 ◽  
Author(s):  
YUANXI XIE
Keyword(s):  
Exact Solutions ◽  
Burgers Equation ◽  
Kdv Equation ◽  
Combination Method ◽  
Generalized Kdv Equation ◽  
Generalized Burgers Equation

In view of the analysis on the characteristics of the generalized Burgers equation, generalized KdV equation and generalized Burgers–KdV equation, a combination method is presented to seek the explicit and exact solutions to the generalized Burgers–KdV equation by combining with those of the generalized Burgers equation and generalized KdV equation. As a result, many explicit and exact solutions for the generalized Burgers–KdV equation are successfully obtained by this technique.

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