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

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	309-316
Number of pages	8
Journal	Chinese Annals of Mathematics. Series B
Volume	33
Issue number	2
DOIs	https://doi.org/10.1007/s11401-012-0696-1
State	Published - Mar 2012

Keywords

Exact solutions
Monge-Ampère equation
Symmetry reduction

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10.1007/s11401-012-0696-1

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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 - 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

SN - 0252-9599

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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

Abstract

Keywords

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