Approximation of the Korteweg-de Vries Equation by the Nonlinear Schrödinger Equation
Approximation of the Korteweg-de Vries Equation by the Nonlinear Schrödinger Equation
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DOI：
10.1006/jdeq.1998.3417
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发表时间：
1998-08
影响因子：
2.4
通讯作者：
G. Schneider
中科院分区：
文献类型：
--
作者：
G. Schneider
1968年Zakharov导出了非线性薛定谔方程作为水波问题的近似方程。水波问题是否真的有解可以用非线性薛定谔方程的解来近似，这是一个有待解决的问题。在回答这个问题的过程中，我们对一个模型问题--用非线性薛定谔方程逼近Korteweg-de弗里斯方程取得了一些进展。
Abstract In 1968 Zakharov derived the Nonlinear Schrodinger equation as an approximation equation for the water wave problem. It is still an open problem if there are really solutions of the water wave problem which can be approximated by the solutions of the Nonlinear Schrodinger equation. In answering this question we made some progress for a model problem—the approximation of the Korteweg–de Vries equation by the Nonlinear Schrodinger equation.