Symmetry reduction and exact solutions of a hyperbolic Monge-Ampère equation

Zhongzhou Dong; Yong Chen; Dexing Kong; Zenggui Wang

doi:10.1007/s11401-012-0696-1

Symmetry reduction and exact solutions of a hyperbolic Monge-Ampère equation

Zhongzhou Dong^*
, Yong Chen
, Dexing Kong
, Zenggui Wang

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

12 引用（Scopus）

摘要

By means of the classical symmetry method, a hyperbolic Monge-Ampère equation is investigated. The symmetry group is studied and its corresponding group invariant solutions are constructed. Based on the associated vector of the obtained symmetry, the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation, from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully.

源语言	英语
页（从-至）	309-316
页数	8
期刊	Chinese Annals of Mathematics. Series B
卷	33
期	2
DOI	https://doi.org/10.1007/s11401-012-0696-1
出版状态	已出版 - 3月 2012

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abstract = "By means of the classical symmetry method, a hyperbolic Monge-Amp{\`e}re equation is investigated. The symmetry group is studied and its corresponding group invariant solutions are constructed. Based on the associated vector of the obtained symmetry, the authors construct the group-invariant optimal system of the hyperbolic Monge-Amp{\`e}re equation, from which two interesting classes of solutions to the hyperbolic Monge-Amp{\`e}re equation are obtained successfully.",

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AU - Dong, Zhongzhou

AU - Chen, Yong

AU - Kong, Dexing

AU - Wang, Zenggui

PY - 2012/3

Y1 - 2012/3

N2 - By means of the classical symmetry method, a hyperbolic Monge-Ampère equation is investigated. The symmetry group is studied and its corresponding group invariant solutions are constructed. Based on the associated vector of the obtained symmetry, the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation, from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully.

AB - By means of the classical symmetry method, a hyperbolic Monge-Ampère equation is investigated. The symmetry group is studied and its corresponding group invariant solutions are constructed. Based on the associated vector of the obtained symmetry, the authors construct the group-invariant optimal system of the hyperbolic Monge-Ampère equation, from which two interesting classes of solutions to the hyperbolic Monge-Ampère equation are obtained successfully.

KW - Exact solutions

KW - Monge-Ampère equation

KW - Symmetry reduction

UR - https://www.scopus.com/pages/publications/84863285939

U2 - 10.1007/s11401-012-0696-1

DO - 10.1007/s11401-012-0696-1

M3 - 文章

AN - SCOPUS:84863285939

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JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 2

ER -

Symmetry reduction and exact solutions of a hyperbolic Monge-Ampère equation

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