scholarly journals Efficient Iterative Method for Solving Korteweg-de Vries Equations

2019 ◽  
pp. 1575-1583
Author(s):  
Samaher marez Yassein ◽  
Asmaa Abd Aswhad
Keyword(s):  
Water Waves ◽  
Vries Equation ◽  
Applied Mathematics ◽  
Travelling Waves ◽  
Approximate Solutions ◽  
Shallow Water Waves ◽  
Fluid Physics ◽  
Linear Partial Differential Equations ◽  
De Vries ◽  
Physical Phenomena

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of non-linear partial differential equations with small amount of computations does not require to calculate restrictive assumptions or transformation like other conventional methods. In addition, several examples clarify the relevant features of this presented method, so the results of this study are debated to show that this method is a powerful tool and promising to illustrate the accuracy and efficiency for solving these problems. To evaluate the results in the iterative process we used the Matlab symbolic manipulator.

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.

The Korteweg-de Vries equation and water waves. Solutions of the equation. Part 1

1973 ◽  
Vol 59 (4) ◽  
pp. 721-736 ◽  
Author(s):  
Harvey Segur
Keyword(s):  
Water Waves ◽  
Large Time ◽  
Vries Equation ◽  
Asymptotic Properties ◽  
Series Representation ◽  
Convergent Series ◽  
Asymptotic Results ◽  
De Vries ◽  
Method Of Solution

The method of solution of the Korteweg–de Vries equation outlined by Gardneret al.(1967) is exploited to solve the equation. A convergent series representation of the solution is obtained, and previously known aspects of the solution are related to this general form. Asymptotic properties of the solution, valid for large time, are examined. Several simple methods of obtaining approximate asymptotic results are considered.

Asymptotic stepwise solutions of the Korteweg--de Vries equation with a singular perturbation and their accuracy

2021 ◽  
Vol 8 (3) ◽  
pp. 410-421
Author(s):  
S. I. Lyashko ◽  
◽  
V. H. Samoilenko ◽  
Yu. I. Samoilenko ◽  
I. V. Gapyak ◽  
...  
Keyword(s):  
Singular Perturbation ◽  
Small Parameter ◽  
Asymptotic Approximation ◽  
Vries Equation ◽  
Approximate Solutions ◽  
Variable Coefficients ◽  
Main Term ◽  
Asymptotic Approximations ◽  
De Vries ◽  
The Given

The paper deals with the Korteweg-de Vries equation with variable coefficients and a small parameter at the highest derivative. The asymptotic step-like solution to the equation is obtained by the non-linear WKB technique. An algorithm of constructing the higher terms of the asymptotic step-like solutions is presented. The theorem on the accuracy of the higher asymptotic approximations is proven. The proposed technique is demonstrated by example of the equation with given variable coefficients. The main term and the first asymptotic approximation of the given example are found, their analysis is done and statement of the approximate solutions accuracy is presented.

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