scholarly journals Computational Analysis of Shallow Water Waves with Korteweg-de Vries Equation

2017 ◽  
Vol 0 (0) ◽  
pp. 0-0 ◽  
Author(s):  
Turgut Ak ◽  
Houria Triki ◽  
Sharanjeet Dhawan ◽  
Samir Kumar Bhowmik ◽  
Seithuti Philemon Moshokoa ◽  
...  
Keyword(s):  
Shallow Water ◽  
Water Waves ◽  
Computational Analysis ◽  
Vries Equation ◽  
Shallow Water Waves ◽  
De Vries

scholarly journals SIMULATION OF KORTEWEG DE VRIES EQUATION

2012 ◽  
Vol 09 ◽  
pp. 574-580
Author(s):  
S. MAT ZIN ◽  
W. N. M. ARIFFIN ◽  
S. A. HASHIM ALI
Keyword(s):  
Mathematical Model ◽  
Shallow Water ◽  
Nonlinear Wave ◽  
Water Waves ◽  
Vries Equation ◽  
Kdv Equation ◽  
Soliton Solutions ◽  
Interaction Process ◽  
Shallow Water Waves ◽  
De Vries

Korteweg de Vries (KdV) equation has been used as a mathematical model of shallow water waves. In this paper, we present one-, two-, and three-soliton solution of KdV equation. By definition, soliton is a nonlinear wave that maintains its properties (shape and velocity) upon interaction with each other. In order to investigate the behavior of soliton solutions of KdV equation and the interaction process of the two- and three-solitons, computer programs have been successfully simulated. Results from these simulations confirm that the solutions of KdV equation obtained are the soliton solutions.

Experiments on strong interactions between solitary waves

1978 ◽  
Vol 85 (3) ◽  
pp. 417-431 ◽  
Author(s):  
P. D. Weidman ◽  
T. Maxworthy
Keyword(s):  
Shallow Water ◽  
Solitary Waves ◽  
Water Waves ◽  
Vries Equation ◽  
Rectangular Channel ◽  
Quantitative Agreement ◽  
Strong Interactions ◽  
Shallow Water Waves ◽  
Qualitative And Quantitative ◽  
The Waves

Experiments on the interaction between solitary shallow-water waves propagating in the same direction have been performed in a rectangular channel. Two methods were devised to compensate for the dissipation of the waves in order to compare results with Hirota's (1971) solution for the collision of solitons described by the Kortewegde Vries equation. Both qualitative and quantitative agreement with theory is obtained using the proposed corrections for wave damping.

Amplification and decay of long nonlinear waves

1973 ◽  
Vol 58 (3) ◽  
pp. 481-493 ◽  
Author(s):  
S. Leibovich ◽  
J. D. Randall
Keyword(s):  
Shallow Water ◽  
Nonlinear Waves ◽  
Water Waves ◽  
Vries Equation ◽  
Variable Coefficients ◽  
Finite Amplitude ◽  
Rotating Fluids ◽  
Shallow Water Waves ◽  
Weakly Nonlinear ◽  
Weakly Nonlinear Waves

The interaction of weakly nonlinear waves with slowly varying boundaries is considered. Special emphasis is given to rotating fluids, but the analysis applies with minor modifications to waves in stratified fluids and shallow-water aves. An asymptotic solution of a variant of the Korteweg–de Vries equation with variable coefficients is developed that produces a ‘Green's law’ for the amplification of waves of finite amplitude. For shallow-water waves in water of variable depth, the result predicts wave growth proportional to the $-\frac{1}{3}$ power of the depth.

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