Asymptotic behavior of the Korteweg–de Vries equation posed in a quarter plane
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چکیده
منابع مشابه
A Non-homogeneous Boundary-value Problem for the Korteweg-de Vries Equation in a Quarter Plane
The Korteweg-de Vries equation was first derived by Boussinesq and Korteweg and de Vries as a model for long-crested small-amplitude long waves propagating on the surface of water. The same partial differential equation has since arisen as a model for unidirectional propagation of waves in a variety of physical systems. In mathematical studies, consideration has been given principally to pure i...
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Laboratory experiments have shown that when nonlinear, dispersive waves are forced periodically from one end of an undisturbed stretch of the medium of propagation, the signal eventually becomes temporally periodic at each spatial point. It is our purpose here to establish this as a fact at least in the context of a damped Korteweg-de Vries equation. Thus, consideration is given to the initial-...
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In [9] and [10], we have studied the initial value problem for the Korteweg-de Vries (KdV) equation (1.1) ut—6uu x +u xxx =0 by the inverse scattering method. In this paper we study the asymptotic behavior of the solutions as t— >zh°°-Consider the Schrodinger equation (1.2) over (— oo } oo) with the potential u(x) satisfying (1.3) (throughout the paper integration is taken over (— oo, oo) unles...
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The initial boundary-value problem for the Korteweg–de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one bo...
متن کاملAn initial-boundary value problem for the Korteweg-de Vries equation on the negative quarter-plane
In this paper, we consider an initial-boundary value problem for the Kortewegde Vries equation on the negative quarter-plane. The normalized Korteweg-de Vries equation considered is given by uτ + uux + uxxx = 0, x < 0, τ > 0, where x and τ represent dimensionless distance and time respectively. In particular, we consider the case when the initial and boundary conditions are given by u(x, 0) = u...
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ژورنال
عنوان ژورنال: Journal of Differential Equations
سال: 2009
ISSN: 0022-0396
DOI: 10.1016/j.jde.2008.11.002