Nonlocal symmetries and exact solutions for PIB equation

Xiang Peng Xin; Qian Miao; Yong Chen

doi:10.1088/0253-6102/58/3/03

Nonlocal symmetries and exact solutions for PIB equation

Xiang Peng Xin^*
, Qian Miao
, Yong Chen

^*Corresponding author for this work

School of Mathematical Sciences

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

8 Scopus citations

Abstract

In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.

Original language	English
Pages (from-to)	331-337
Number of pages	7
Journal	Communications in Theoretical Physics
Volume	58
Issue number	3
DOIs	https://doi.org/10.1088/0253-6102/58/3/03
State	Published - Sep 2012

Keywords

classical Lie symmetry method
explicit solution
nonlocal symmetry
optimal system

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10.1088/0253-6102/58/3/03

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title = "Nonlocal symmetries and exact solutions for PIB equation",

abstract = "In this paper, the symmetry group of the (2+1)-dimensional Painlev{\'e} integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.",

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AU - Miao, Qian

AU - Chen, Yong

PY - 2012/9

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N2 - In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.

AB - In this paper, the symmetry group of the (2+1)-dimensional Painlevé integrable Burgers (PIB) equations is studied by means of the classical symmetry method. Ignoring the discussion of the infinite-dimensional subalgebra, we construct an optimal system of one-dimensional group invariant solutions. Furthermore, by using the conservation laws of the reduced equations, we obtain nonlocal symmetries and exact solutions of the PIB equations.

KW - classical Lie symmetry method

KW - explicit solution

KW - nonlocal symmetry

KW - optimal system

UR - https://www.scopus.com/pages/publications/84866398795

U2 - 10.1088/0253-6102/58/3/03

DO - 10.1088/0253-6102/58/3/03

M3 - 文章

AN - SCOPUS:84866398795

SN - 0253-6102

VL - 58

SP - 331

EP - 337

JO - Communications in Theoretical Physics

JF - Communications in Theoretical Physics

IS - 3

ER -

Nonlocal symmetries and exact solutions for PIB equation

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Keywords

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