The Korteweg–de Vries (KdV) Equation
The origins of the Korteweg-De Vries equation: Collaboration between Korteweg and De Vries
... The Korteweg-De Vries equation that describes the behaviour of long wavelength waves in shallow water has generated an extensive body of literature since Zabus- ky and Kruskal rediscovered it ...
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Numerical Solution of The Korteweg de Vries Equation
... J. Phys. 60, 650. USA. [3]. Johnson RS, 1994, Solitary wave, solution and shelf evolution over variable depth, J. fluid. Mech. 276, 125-138, Cambridge University, USA. [4]. Soewono E, Andonowati, SR. Pudjaprasetya, HJ. ...
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PT-symmetric deformations of the Korteweg-de Vries equation
... Centre for Mathematical Science, City University Northampton Square, London EC1V 0HB, UK E-mail: [email protected] Abstract: We propose a new family of complex PT -symmetric extensions of the Korteweg-de ...
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The Korteweg de Vries equation and a Diophantine problem related to Bernoulli polynomials
... and applications of the Korteweg-de Vries equation, we refer to [, ] and [] and the ref- erences given therein. Using the spectral theory of Schrödinger operators, see [], Fairlie and ...
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Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain
... the Korteweg-de Vries equation on a finite ...the Korteweg-de Vries equation on a finite ...the Korteweg-de Vries equation and the ...
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Control and Stabilization of the Korteweg-de Vries Equation on a Periodic Domain
... KdV equation has been intensively studied from various aspects of both mathematics and physics since the 1960s when solitons were dis- covered through solving the KdV equation, and the inverse scattering ...
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Numerical inverse scattering for the Korteweg–-de Vries and modified Korteweg–-de Vries equations
... the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary ...
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The Korteweg-De Vries Equation and its Homologues: A Comparative Analysis II
... Thus, it is necessary to establish well-posec1ness, the existence of solitary wave and other elementary solut10ns and the existence of other properties such as, f[r] ...
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Existence for Korteweg de Vries type equation with delay
... the Korteweg-de vries ...DJ, De Vries, G: On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary ...
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The Pfaffian Technique: A (2 + 1) Dimensional Korteweg de Vries Equation
... the Korteweg de Vries equation, the Sin-Gordon equation, the nonlinear Schrödinger equ- ation, the Kadomtsev-Petviashvili equation, the Davey-Stewartson equation, ...
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Soliton solutions for Korteweg-de Vries equation by homotopy analysis method
... Among many nonlinear equations in physics, The Korteweg-de Vries (kdv) equation is a typical, relatively simple and classical one. It is a well- known mathematical model of nonlinear waves on ...
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Solving Variable Coefficient Korteweg-de Vries Equation Using Pseudospectral Method
... The Korteweg-de Vries (KdV) equation which is well established as a model for weakly nonlinear long waves is first derived by Korteweg and de Vries ( 1895) governing long ...
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Sinc collocation linked with finite differences for Korteweg-de Vries Fractional Equation
... nonlinear equation admits traveling wave solutions of different ...the Korteweg-de Vries equation is the soliton, or solitary ...same equation (3) has also come up in the theory ...
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An Unconventional Splitting for Korteweg de Vries-Burgers Equation
... the Korteweg de Vries–Burgers (KdVB) equation based on splitting is ...KdVB equation and split the equation into two ...KdVB equation enables us to play with the splitted ...
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The Sylvester equation and the elliptic Korteweg-de Vries system
... VIII. CONCLUSIONS In this paper a new class of solutions of the elliptic KdV systems (both the discrete (1.1) and the continuous (1.2)) has been uncovered. We made use of Sylvester-type equation with elliptic ...
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Approximate solution of forced korteweg-de vries equation
... on Korteweg- de Vries (KdV) equation and they were able to get free solitons generated, Shen (1993) ...KdV equation, it has lost group symmetries and the traditional group-theoretical ...
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PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
... A few comments are in order: There are of course various other options, as for instance to deform only one of the last two terms in (2.39), possibly together with the first term. This would lead to a rather strange ...
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Martingale Solution to Stochastic Extended Korteweg de Vries Equation
... KdV equation seems to be considering stochastic versions of such ...KdV2 equation driven by random noise can be a model of several kinds of waves ...KdV2 equation are possible: the case with additive ...
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CiteSeerX — CONVERGENCE OF NUMERICAL SCHEMES FOR THE KORTEWEG-DE VRIES-KAWAHARA EQUATION.
... In [1], authors have considered a fully-discrete finite difference scheme for the KdV equation and showed the convergence of their scheme. In this paper, we are going to use a similar technique here. Note that Sj¨ ...
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Three dimensional Korteweg de Vries equation and traveling wave solutions
... this equation, x is the direction of propagation while y and z are transverse ...KdV equation with f (u) = u n , where n is a positive integer. This equation is thus called the three- dimensional ...
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