Zhang Da-jun, Jian-bing Zhang, Qing Shen, “A limit symmetry of the Korteweg–de Vries equation and its applications”, TMF, 2010, Volume 163, Number 2,Pages <nobr>277

This article is cited in 7 papers

A limit symmetry of the Korteweg–de Vries equation and its applications

Zhang Da-jun^a, Jian-bing Zhang^ba, Qing Shen^a

^a Department of Mathematics, Shanghai University, Shanghai, China
^b School of Mathematics Science, Xuzhou Normal University, Xuzhou, China

Abstract: We discuss a symmetry of the Korteweg–de Vries (KdV) equation. This symmetry can be related to the squared eigenfunction symmetry by a limit procedure. As applications, we consider the similarity reduction of the KdV equation and a KdV equation with new self-consistent sources. We derive some solutions via a bilinear approach.

Keywords: symmetry, KdV equation, symmetry constraint, self-consistent source, bilinear method.

Received: 29.09.2009

DOI: 10.4213/tmf6499