Modulational instability of cnoidal wave solutions of the modified Korteweg–de Vries equation

1976 ◽  
Vol 17 (7) ◽  
pp. 1196-1200 ◽  
Author(s):  
C. F. Driscoll ◽  
T. M. O’Neil
Keyword(s):  
Vries Equation ◽  
Modulational Instability ◽  
Cnoidal Wave ◽  
Wave Solutions ◽  
De Vries

scholarly journals Three-dimensional Korteweg-de Vries equation and traveling wave solutions

2000 ◽  
Vol 24 (6) ◽  
pp. 379-384 ◽  
Author(s):  
Kenneth L. Jones
Keyword(s):  
Vries Equation ◽  
Three Dimensional ◽  
Traveling Wave Solutions ◽  
Summation Formula ◽  
Cnoidal Wave ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
De Vries ◽  
Infinite Sums ◽  
Poisson’S Summation Formula

The three-dimensional power Korteweg-de Vries equation[ut+unux+uxxx]x+uyy+uzz=0, is considered. Solitary wave solutions for any positive integernand cnoidal wave solutions forn=1andn=2are obtained. The cnoidal wave solutions are shown to be represented as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.

scholarly journals Nearly conconcentric Korteweg-de Vries equation and periodic traveling wave solution

1998 ◽  
Vol 21 (1) ◽  
pp. 183-187
Author(s):  
Yunkai Chen
Keyword(s):  
Vries Equation ◽  
Summation Formula ◽  
Traveling Wave Solution ◽  
Cnoidal Wave ◽  
Wave Solutions ◽  
Petviashvili Equation ◽  
De Vries ◽  
Periodic Traveling Wave ◽  
Infinite Sums ◽  
Poisson’S Summation Formula

The generalized nearly concentric Korteweg-de Vries equation[un+u/(2η)+u2uζ+uζζζ]ζ+uθθ/η2=0is considered. The author converts the equation into the power Kadomtsev-Petviashvili equation[ut+unux+uxxx]x+uyy=0. Solitary wave solutions and cnoidal wave solutions are obtained. The cnoidal wave solutions are shown to be representable as infinite sums of solitons by using Fourier series expansions and Poisson's summation formula.

Abundant rogue wave solutions for the (2 + 1)-dimensional generalized Korteweg–de Vries equation

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Huanhuan Lu ◽  
Yufeng Zhang
Keyword(s):  
Vries Equation ◽  
Rogue Wave ◽  
Rogue Waves ◽  
Third Order ◽  
First Order ◽  
Wave Solutions ◽  
De Vries ◽  
Rogue Wave Solutions ◽  
Bilinear Formulation ◽  
Hirota Bilinear

AbstractIn this paper, we analyse two types of rogue wave solutions generated from two improved ansatzs, to the (2 + 1)-dimensional generalized Korteweg–de Vries equation. With symbolic computation, the first-order rogue waves, second-order rogue waves, third-order rogue waves are generated directly from the first ansatz. Based on the Hirota bilinear formulation, another type of one-rogue waves and two-rogue waves can be obtained from the second ansatz. In addition, the dynamic behaviours of obtained rogue wave solutions are illustrated graphically.

Cnoidal Wave Trains and Solitary Waves in a Dissipation-Modified Korteweg—de Vries Equation

KdV ’95 ◽  
1995 ◽  
pp. 457-475
Author(s):  
A. Ye. Rednikov ◽  
M. G. Velarde ◽  
Yu. S. Ryazantsev ◽  
A. A. Nepomnyashchy ◽  
V. N. Kurdyumov
Keyword(s):  
Solitary Waves ◽  
Vries Equation ◽  
Cnoidal Wave ◽  
De Vries ◽  
Wave Trains
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