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Korteweg–de Vries equations

Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg De Vries Equations

Discrete Singular Convolution Method for Numerical Solutions of Fifth Order Korteweg De Vries Equations

... differential equations (PDEs) is the major subject in many fields of physical and nonlinear ...order Korteweg-de Vries equations ...

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Existence and stability of solitary waves for the generalized Korteweg-de Vries equations

Existence and stability of solitary waves for the generalized Korteweg-de Vries equations

... fractional Korteweg-de Vries equations with general ...generalized Korteweg-de Vries equations under some assumptions of the nonlinear ...the equations, in ...

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Application of Hyperbola Function Method to the Family of Third Order Korteweg de Vries Equations

Application of Hyperbola Function Method to the Family of Third Order Korteweg de Vries Equations

... In this work, we apply a hyperbola function method to solve the nonlinear family of third order Korteweg-de Vries equations. Exact travelling wave solutions are obtained and expressed in terms ...

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Numerical investigations of waves interactions from forced Korteweg de Vries equations

Numerical investigations of waves interactions from forced Korteweg de Vries equations

... The transcritical flow over a step has been studied using the fKdV equation. Zhang and Zhu (1997) integrated the time-dependent forced KdV equation numerically and found steady transcritical flows for negative forcing. ...

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Travelling Solitary Wave Solutions to Higher Order Korteweg de Vries Equation

Travelling Solitary Wave Solutions to Higher Order Korteweg de Vries Equation

... Usually m is a positive integer, however, once in a while, the value of m is a neg- ative or a fraction, the other kinds of expression will introduced. In the following, we illustrate the method by using it to solve the ...

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Numerical Simulation for Nonlinear Water Waves Propagating along the Free Surface

Numerical Simulation for Nonlinear Water Waves Propagating along the Free Surface

... differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term and also it reduces the size of calculations besides, its interactions are direct and straightforward ...

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Korteweg de Vries description of Helmholtz Kerr dark solitons

Korteweg de Vries description of Helmholtz Kerr dark solitons

... universal equations in the form of the well-known Zakharov equations of plasma ...Bloch equations may be reduced to a complex Ginzburg-Landau ...

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Approximate solution of forced korteweg-de vries equation

Approximate solution of forced korteweg-de vries equation

... Abstract Several findings on forced solitons generated by the forced Korteweg- de Vries equation (fKdV) are discussed in this paper. This equation has lost group symmetries due to the forcing term. ...

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Adomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation

Adomian Polynomial and Elzaki Transform Method of Solving Fifth Order Korteweg-De Vries Equation

... In this paper, Elzaki transform and Adomian polynomial have been effectively used to solve nonlinear fifth order Korteweg-de Vries (KdV) equations. The solutions obtained were presented in ...

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The Korteweg de Vries equation and a Diophantine problem related to Bernoulli polynomials

The Korteweg de Vries equation and a Diophantine problem related to Bernoulli polynomials

... three equations are elliptic Diophantine equa- tions, thus using the program package MAGMA, subroutines IntegralPoints or IntegralQuarticPoints are just a straightforward calculation to solve ...

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PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation

PT-symmetric extensions of the supersymmetric Korteweg-de Vries equation

... Clearly with regard to these new models there are many interesting questions left to be explored. It remains to be settled whether these models possess non-trivial higher charges and if the conservation laws survive the ...

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PT-symmetric deformations of the Korteweg-de Vries equation

PT-symmetric deformations of the Korteweg-de Vries equation

... We shall now construct solutions of the equations of motion (3.5). One may expect to find a rich variety of different types of solutions similarly as for the standard KdV equation. Over the years several methods ...

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Hyperbolic Tangent ansatz method to space time fractional modified KdV, modified EW and Benney–Luke Equations

Hyperbolic Tangent ansatz method to space time fractional modified KdV, modified EW and Benney–Luke Equations

... fractional Korteweg-de Vries equation, modified Equal Width equation and Benney-Luke Equations are solved by using simple hyperbolic tangent Ansatz ...governing equations to integer ...

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An Unconventional Splitting for Korteweg de Vries-Burgers Equation

An Unconventional Splitting for Korteweg de Vries-Burgers Equation

... ferential equations and applying appropriate numerical integrators for each part (see [11, 15] and references ...the equations into two parts both of which are KdVB ...

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Martingale Solution to Stochastic Extended Korteweg de Vries Equation

Martingale Solution to Stochastic Extended Korteweg de Vries Equation

... The existence of martingale solution to highly nonlinear extended KdV equations is proved for all physically relevant initial conditions. The presence of several nonlinear terms in the considered equation required ...

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Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

Modelling and nonlinear boundary stabilization of the modified generalized Korteweg–de Vries–Burgers equation

... dimensionless equations to show the propagation of small but finite am- plitude wave in a prestressed thick viscoelastic tube that was filled with a viscous fluid ...

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Some traveling wave solutions of soliton family

Some traveling wave solutions of soliton family

... the Korteweg-de Vries (KdV), Modified Korteweg-de Vries (mKdV) and Regularised Long Wave (RLW) equations using Homotopy Perturbation method ...

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Simplest Equation Method for nonlinear solitary waves in Thomas- Fermi plasmas

Simplest Equation Method for nonlinear solitary waves in Thomas- Fermi plasmas

... differential equations as Korteweg-de-Vries equation [8], modified Kortewegde-Vries (mKdV) equation [18] and the nonlinear Schrodinger equation (NLSE) [6, 17] investigated effects of ...

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Exact Solution and Conservation Laws for Fifth Order Korteweg de Vries Equation

Exact Solution and Conservation Laws for Fifth Order Korteweg de Vries Equation

...  V G ,  are functions of x t , and derivatives of . The equality (2) is assumed to be satisfied for any solution of the corresponding system of equations, is called conserved density and G is called conserved ...

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Water waves and Integrability

Water waves and Integrability

... that equations, containing nonlinearities as those, appearing in the equations of Camassa & Holm (1993), Fokas & Fuchssteiner (1981) [called also CH from now on] and Degasperis & Procesi (1999), ...

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