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

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

中国物理B ›› 2010, Vol. 19 ›› Issue (4): 40201-040201.doi: 10.1088/1674-1056/19/4/040201

• GENERAL • 下一篇

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

李志芳, 阮航宇

Department of Physics, Ningbo University, Ningbo 315211, China

收稿日期:2009-08-08 修回日期:2009-09-08 出版日期:2010-04-15 发布日期:2010-04-15
基金资助:
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).

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

Li Zhi-Fang(李志芳)^† and Ruan Hang-Yu(阮航宇)

Department of Physics, Ningbo University, Ningbo 315211, China

Received:2009-08-08 Revised:2009-09-08 Online:2010-04-15 Published:2010-04-15
Supported by:
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).

摘要/Abstract

摘要： 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.

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.

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

中图分类号: (Solitons)

05.45.Yv

02.30.Jr (Partial differential equations) 02.20.Sv (Lie algebras of Lie groups)

李志芳, 阮航宇. The extended symmetry approach for studying the general Korteweg-de Vries-type equation[J]. 中国物理B, 2010, 19(4): 40201-040201.

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[J]. Chin. Phys. B, 2010, 19(4): 40201-040201.

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

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

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