A Class of PDEs with Nonlinear Superposition Principles

Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the go...

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Main Authors: Li Peng, Liu Keying, Pan Zuliang, Zhong Weizhou
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/346824
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spelling doaj-6340c16a95824169a68282c82d8df7242020-11-24T23:17:08ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/346824346824A Class of PDEs with Nonlinear Superposition PrinciplesLi Peng0Liu Keying1Pan Zuliang2Zhong Weizhou3Department of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, ChinaDepartment of Mathematics, North China University of Water Conservancy and Electric Power, Zhengzhou 450011, ChinaDepartment of Mathematics, Zhejiang University, Hangzhou 310027, ChinaSchool of Economics and Finance, Xi’an Jiaotong University, Xi’an 710061, ChinaThrough assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.http://dx.doi.org/10.1155/2012/346824
collection DOAJ
language English
format Article
sources DOAJ
author Li Peng
Liu Keying
Pan Zuliang
Zhong Weizhou
spellingShingle Li Peng
Liu Keying
Pan Zuliang
Zhong Weizhou
A Class of PDEs with Nonlinear Superposition Principles
Journal of Applied Mathematics
author_facet Li Peng
Liu Keying
Pan Zuliang
Zhong Weizhou
author_sort Li Peng
title A Class of PDEs with Nonlinear Superposition Principles
title_short A Class of PDEs with Nonlinear Superposition Principles
title_full A Class of PDEs with Nonlinear Superposition Principles
title_fullStr A Class of PDEs with Nonlinear Superposition Principles
title_full_unstemmed A Class of PDEs with Nonlinear Superposition Principles
title_sort class of pdes with nonlinear superposition principles
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description Through assuming that nonlinear superposition principles (NLSPs) are embedded in a Lie group, a class of 3rd-order PDEs is derived from a general determining equation that determine the invariant group. The corresponding NLSPs and transformation to linearize the nonlinear PDE are found, hence the governing PDE is proved C-integrable. In the end, some applications of the PDEs are explained, which shows that the result has very subtle relations with linearization of partial differential equation.
url http://dx.doi.org/10.1155/2012/346824
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