The extended symmetry approach for studying the general Korteweg-de Vries-type equation

doi:10.1088/1674-1056/19/4/040201

Abstract The extended symmetry approach is used to study the general Korteweg-de Vries-type (KdV-type) equation. Several variable-coefficient equations are obtained. The solutions of these resulting equations can be constructed by the solutions of original models if their solutions are well known, such as the standard constant coefficient KdV equation and the standard compound KdV--Burgers equation, and so on. Then any one of these variable-coefficient equations can be considered as an original model to obtain new variable-coefficient equations whose solutions can also be known by means of transformation relations between solutions of the resulting new variable-coefficient equations and the original equation.

Keywords: extended symmetry approach general Korteweg-de Vries-type (KdV-type) equation variable-coefficient equation

Received: 08 August 2009
Revised: 08 September 2009
Accepted manuscript online:

PACS:	05.45.Yv	(Solitons)
	02.30.Jr	(Partial differential equations)
	02.20.Sv	(Lie algebras of Lie groups)

Fund: Project supported by the National Natural Science Foundation of China (Grant No.~10675065) and the Scientific Research Fund of the Education Department of Zhejiang Province of China (Grant No.~20070979).

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Li Zhi-Fang(李志芳) and Ruan Hang-Yu(阮航宇) The extended symmetry approach for studying the general Korteweg-de Vries-type equation 2010 Chin. Phys. B 19 040201

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The extended symmetry approach for studying the general Korteweg-de Vries-type equation

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