KdV Limit for the One-dimensional Shallow Water Type System

LEI Xiaohui

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KdV Limit for the One-dimensional Shallow Water Type System

LEI Xiaohui *

Department of Mathematics, Chongqing University, Chongqing 400044

*Correspondence author

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Funding: none

Opened online: 2 February 2018

Accepted by: none

Citation: LEI Xiaohui.KdV Limit for the One-dimensional Shallow Water Type System[OL]. [ 2 February 2018] http://en.paper.edu.cn/en_releasepaper/content/4743420

In this paper, we consider the KdV limit for the one-dimensional shallow water type equation with a special stress force. Under the Gardner-Morikawa transform, we establish that the solutions of such shallow water type system converge to the KdV equation as $\varepsilon\to 0$. This justifies rigorously the KdV limit of the shallow water type equation.

Keywords:Korteweg-de Vries equation; shallow water equation; long wavelength limit; reductive pertuebation method

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