KdV方程 Korteweg–de Vries equation
（重定向自KdV equation）
KdV方程是1895年由荷兰数学家科特韦格和德弗里斯共同发现的一种偏微分方程（也有人称之为科特韦格-德弗里斯方程，但一般都习惯直接叫KdV方程）。关于实自变量x 和t 的函数φ所满足的KdV方程形式如下：
KdV方程的解为簇集的孤立子（又称孤子，孤波）。
KdV equation
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Korteweg–de Vries equation KdV方程
（重定向自KdV equation）
![Numerical solution of the KdV equation ut + uux + δ2uxxx = 0 (δ = 0.022) with an initial condition u(x, 0) = cos(πx). Its calculation was done by the Zabusky–Kruskal scheme.[1] The initial cosine wave evolves into a train of solitary-type waves.](/uploads/202501/22/KdV_equation1112.gif)
In mathematics, the Korteweg–de Vries equation (KdV equation for short) is a mathematical model of waves on shallow water surfaces. It is particularly notable as the prototypical example of an exactly solvable model, that is, a non-linear partial differential equation whose solutions can be exactly and precisely specified. KdV can be solved by means of the inverse scattering transform. The mathematical theory behind the KdV equation is a topic of active research. The KdV equation was first introduced by Boussinesq (1877,footnote on page 360) and rediscovered by DiederikKortewegandGustav de Vries (1895).
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