A numerical study of the long-wave short-wave resonance for 3D water waves

2001 ◽  
Vol 20 (5) ◽  
pp. 627-650 ◽  
Author(s):  
Christophe Besse ◽  
David Lannes
Keyword(s):  
Water Waves ◽  
Numerical Study ◽  
Short Wave ◽  
Long Wave ◽  
Wave Resonance

Modeling internal rogue waves in a long wave-short wave resonance framework

2018 ◽  
Vol 3 (12) ◽  
Author(s):  
H. N. Chan ◽  
R. H. J. Grimshaw ◽  
K. W. Chow
Keyword(s):  
Rogue Waves ◽  
Short Wave ◽  
Long Wave ◽  
Wave Resonance

On the modulation of water waves on shear flows

1976 ◽  
Vol 347 (1651) ◽  
pp. 537-546 ◽  
Keyword(s):  
Water Waves ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Vries Equation ◽  
Harmonic Wave ◽  
Short Wave ◽  
Long Wave ◽  
Stokes Waves ◽  
The Stability ◽  
Wave Limit

The method of multiple scales is used to examine the slow modulation of a harmonic wave moving over the surface of a two dimensional channel. The flow is assumed inviscid and incompressible, but the basic flow takes the form of an arbitrary shear. The appropriate nonlinear Schrödinger equation is derived with coefficients that depend, in a complicated way, on the shear. It is shown that this equation agrees with previous work for the case of no shear; it also agrees in the long wave limit with the appropriate short wave limit of the Korteweg-de Vries equation, the shear being arbitrary. Finally, it is remarked that the stability of Stokes waves over any shear can be examined by using the results derived here.

Application of the Weierstrass Elliptic Expansion Method to the Long-Wave and Short-Wave Resonance Interaction System

2008 ◽  
Vol 63 (5-6) ◽  
pp. 273-279 ◽  
Author(s):  
Xian-Jing Lai ◽  
Jie-Fang Zhang ◽  
Shan-Hai Mei
Keyword(s):  
Periodic Solutions ◽  
Elliptic Function ◽  
Expansion Method ◽  
Short Wave ◽  
Resonance Interaction ◽  
Solitary Wave Solutions ◽  
Jacobian Elliptic Function ◽  
Weierstrass Elliptic Function ◽  
Long Wave ◽  
Wave Resonance

With the aid of symbolic computation, nine families of new doubly periodic solutions are obtained for the (2+1)-dimensional long-wave and short-wave resonance interaction (LSRI) system in terms of the Weierstrass elliptic function method. Moreover Jacobian elliptic function solutions and solitary wave solutions are also given as simple limits of doubly periodic solutions.

scholarly journals Dynamics of solitons in multicomponent long wave–short wave resonance interaction system

Pramana ◽  
2015 ◽  
Vol 84 (3) ◽  
pp. 327-338 ◽  
Author(s):  
T KANNA ◽  
K SAKKARAVARTHI ◽  
M VIJAYAJAYANTHI ◽  
M LAKSHMANAN
Keyword(s):  
Short Wave ◽  
Resonance Interaction ◽  
Long Wave ◽  
Interaction System ◽  
Wave Resonance

scholarly journals Rogue Wave Modes for the Long Wave–Short Wave Resonance Model

2013 ◽  
Vol 82 (7) ◽  
pp. 074001 ◽  
Author(s):  
Kwok Wing Chow ◽  
Hiu Ning Chan ◽  
David Jacob Kedziora ◽  
Roger Hamilton James Grimshaw
Keyword(s):  
Rogue Wave ◽  
Short Wave ◽  
Resonance Model ◽  
Long Wave ◽  
Wave Resonance ◽  
Wave Modes
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