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KdV Equation (kdv + equation)

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Mathematics and Statistics100%

Selected Abstracts

Numerical solution to a linearized KdV equation on unbounded domain

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2008
Chunxiong Zheng
Abstract Exact absorbing boundary conditions for a linearized KdV equation are derived in this paper. Applying these boundary conditions at artificial boundary points yields an initial-boundary value problem defined only on a finite interval. A dual-Petrov-Galerkin scheme is proposed for numerical approximation. Fast evaluation method is developed to deal with convolutions involved in the exact absorbing boundary conditions. In the end, some numerical tests are presented to demonstrate the effectiveness and efficiency of the proposed method.© 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2008 [source]

Variational iteration method for solving the space- and time-fractional KdV equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008
Shaher Momani
Abstract This paper presents numerical solutions for the space- and time-fractional Korteweg,de Vries equation (KdV for short) using the variational iteration method. The space- and time-fractional derivatives are described in the Caputo sense. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and accurate when applied to space- and time-fractional KdV equations. The method introduces a promising tool for solving many space,time fractional partial differential equations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]

Long-time dynamics of KdV solitary waves over a variable bottom

COMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 6 2006
Steven I. Dejak
We study the variable-bottom, generalized Korteweg,de Vries (bKdV) equation ,tu = ,,x(,u + f(u) , b(t,x)u), where f is a nonlinearity and b is a small, bounded, and slowly varying function related to the varying depth of a channel of water. Many variable-coefficient KdV-type equations, including the variable-coefficient, variable-bottom KdV equation, can be rescaled into the bKdV. We study the long-time behavior of solutions with initial conditions close to a stable, b = 0 solitary wave. We prove that for long time intervals, such solutions have the form of the solitary wave whose center and scale evolve according to a certain dynamical law involving the function b(t,x) plus an H1(,)-small fluctuation. © 2005 Wiley Periodicals, Inc. [source]

Homotopy perturbation method for numerical solutions of KdV-Burgers' and Lax's seventh-order KdV equations

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 5 2010
Ahmet Yildirim
Abstract In this article, we applied homotopy perturbation method to obtain the solution of the Korteweg-de Vries Burgers (for short, KdVB) and Lax's seventh-order KdV (for short, LsKdV) equations. The numerical results show that homotopy perturbation method can be readily implemented to this type of nonlinear equations and excellent accuracy. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source]

Variational iteration method for solving the space- and time-fractional KdV equation

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 1 2008
Shaher Momani
Abstract This paper presents numerical solutions for the space- and time-fractional Korteweg,de Vries equation (KdV for short) using the variational iteration method. The space- and time-fractional derivatives are described in the Caputo sense. In this method, general Lagrange multipliers are introduced to construct correction functionals for the problems. The multipliers in the functionals can be identified optimally via variational theory. The iteration method, which produces the solutions in terms of convergent series with easily computable components, requiring no linearization or small perturbation. The numerical results show that the approach is easy to implement and accurate when applied to space- and time-fractional KdV equations. The method introduces a promising tool for solving many space,time fractional partial differential equations. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2007 [source]