The Quasi-Periodic Solutions for the Variable-Coefficient KdV Equation

2012 ◽  
Vol 58 (4) ◽  
pp. 475-479 ◽  
Author(s):  
Feng-Jiao Ouyang ◽  
Shu-Fang Deng
Keyword(s):  
Periodic Solutions ◽  
Variable Coefficient ◽  
Kdv Equation

Periodic and decay mode solutions of the generalized variable-coefficient Korteweg–de Vries equation

2019 ◽  
Vol 33 (20) ◽  
pp. 1950234 ◽  
Author(s):  
Yufeng Zhang ◽  
Jiangen Liu
Keyword(s):  
Periodic Solutions ◽  
Decay Mode ◽  
Variable Coefficient ◽  
Vries Equation ◽  
Kdv Equation ◽  
Variation Of Parameters ◽  
Triply Periodic ◽  
De Vries ◽  
Mode Solution ◽  
First Time

In this paper, we can obtain periodic and decay mode solutions of the generalized variable-coefficient Korteweg–de Vries (gvc-KdV) equation for the first time by using the multivariate transformation technique. Periodic solutions are doubly and triply periodic solutions, and the decay mode solutions include the 1-decay solution and the 2-decay mode solution. Furthermore, we will also study the effect of variation of parameters for solutions systematically, relating to different forms of expression, through graphic display.

Finite-gap periodic solutions of the KdV equation are non-degenerate

1991 ◽  
Vol 161 (3) ◽  
pp. 274-276 ◽  
Author(s):  
A.I. Bobenko ◽  
S.B. Kuksin
Keyword(s):  
Periodic Solutions ◽  
Kdv Equation ◽  
The Kdv Equation
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