DE-VRIES EQUATION
New Energy-Preserving Finite Volume Element Scheme for the Korteweg-de Vries Equation
... Abstract—In this paper, an energy-preserving finite volume element scheme is proposed for the Korteweg-de Vries equation. The scheme is a combination of the discrete variational deriva- tive method ...
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The origins of the Korteweg-De Vries equation: Collaboration between Korteweg and De Vries
... 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 in 1965, ...
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Martingale Solution to Stochastic Extended Korteweg de Vries Equation
... Korteweg-de Vries equation plays an essential role in the description of the creation and propagation of nonlinear waves in many ...Korteweg-de Vries equation dri- ven by a ...
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The Pfaffian Technique: A (2 + 1) Dimensional Korteweg de Vries Equation
... 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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Three dimensional Korteweg de Vries equation and traveling wave solutions
... Abstract. The three-dimensional power Korteweg-de Vries equation [u t +u n u x +u xxx ] x + u yy + u zz = 0, is considered. Solitary wave solutions for any positive integer n and cnoidal wave ...
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Travelling Solitary Wave Solutions to Higher Order Korteweg de Vries Equation
... The travelling solitary wave solutions to the higher order Korteweg-de Vries equation are obtained by using tanh-polynomial method. The method is ef- fective and concise, which is also applied to ...
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Approximate solution of forced korteweg-de vries equation
... Korteweg- de Vries equation (fKdV) are discussed in this ...This equation has lost group symmetries due to the forcing ...fKdV equation and generate uniform forced ...
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Symmetry properties of a generalized Korteweg de Vries equation and some explicit solutions
... Korteweg-de Vries equation and several classes of group invariant solutions for it are obtained by means of this ...generalized equation can be reduced to a first-order equation under a ...
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Lipschitz stability in an inverse problem for the Korteweg-de Vries equation on a finite domain
... measurements of the solution on a part of the boundary and also at some positive time in the whole space domain. The Lipschitz stability of this inverse problem relies on a Carleman estimate for the linearized ...
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A Class of Momentum-Preserving Fourier Pseudo-Spectral Schemes for the Korteweg-de Vries Equation
... The focus of the present paper is on the momentum- preserving schemes, which is based on the second Hamil- tonian system, i.e., Eq. (3). To our knowledge, the scheme has been considered in the context of multi-symplectic ...
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PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation
... Abstract: We discuss several PT -symmetric deformations of superderivatives. Based on these various possibilities, we propose new families of complex PT -symmetric defor- mations of the supersymmetric Korteweg-de ...
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The Korteweg-De Vries Equation and its Homologues: A Comparative Analysis II
... 2.3 Classi fication 33 2.4 Conclusion 36 CHAPTER THREE REVIEW OF THE KORTEWEG-DE VRIES EQUATION 38 3.1 Existence of solitary and periodic wave solutions 38 3.2 Stability of the solitary [r] ...
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Numerical Solution of The Korteweg de Vries Equation
... The solution of the equation (1) are obtained by assuming an ansatz [9], [10]. This ansatz is representation of wave packet (η(ζ)) as a function of range (χ) in secant hyperbolic from which treats time( ) as ...
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The Korteweg de Vries equation and a Diophantine problem related to Bernoulli polynomials
... respectively. One can see that the first three equations are elliptic Diophantine equa- tions, thus using the program package MAGMA, subroutines IntegralPoints or IntegralQuarticPoints are just a straightforward ...
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Solving Variable Coefficient Korteweg-de Vries Equation Using Pseudospectral Method
... Eq. (1) is equivalent to (2) for the case when all coefficients are constant and 𝑄 𝑥 = 0 . However, in the case of water waves in the coastal oceans, there is a need to consider the variation of the background topography ...
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Hirota bilinear computation of multi soliton solutions korteweg de vries equation
... Korteweg de-Vries (KdV) ...the equation was nonlinear, the solitary waves described by Korteweg de Vries (KdV) equation appeared as if they did not interact with each ...Korteweg ...
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Nearly conconcentric Korteweg de Vries equation and periodic traveling wave solution
... 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 a[r] ...
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Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation
... In this paper, we applied the DT to construct the higher-order RW-type rational solutions as well as the evolution of rogue waves for the complex mKdV equation. Based on detailed numerical and analytical ...
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Exact Solution and Conservation Laws for Fifth Order Korteweg de Vries Equation
... With the rapid development of science and technology, the study kernel of modern science is changed from lin- ear to nonlinear step by step. Many nonlinear science problems can simply and exactly be described by using ...
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Interaction of Two Pulsatory Waves of the Korteweg de Vries Equation in a Zigzag Hyperbolic Structure
... A new exact solution for nonlinear interaction of two pulsatory waves of the Korteweg-de Vries (KdV) equation is computed by decomposition in an invariant zigzag hyperbolic tangent (ZHT) structure. A ...
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