PDEPtest: A package for the Painlevé test of nonlinear partial differential equations

Gui Qiong Xu; Zhi Bin Li

doi:10.1016/j.amc.2004.10.055

PDEPtest: A package for the Painlevé test of nonlinear partial differential equations

Gui Qiong Xu, Zhi Bin Li

School of Mathematical Sciences

Shanghai University

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

16 Scopus citations

Abstract

The so-called WTC-Kruskal algorithm is presented in order to study the Painlevé integrability of nonlinear partial differential equations, which combines the WTC method and Kruskal's simplification method. Based on the WTC, Kruskal and WTC-Kruskal algorithms, we give an implementation in Maple called PDEPtest. This package can handle nonlinear partial differential equations which can be transformed to polynomial ones, and its effectiveness is illustrated by applying it to a variety of equations. Some new results are reported.

Original language	English
Pages (from-to)	1364-1379
Number of pages	16
Journal	Applied Mathematics and Computation
Volume	169
Issue number	2
DOIs	https://doi.org/10.1016/j.amc.2004.10.055
State	Published - 15 Oct 2005

Keywords

Kruskal's simplification
Nonlinear partial differential equations
Painlevé test
Symbolic computation
The WTC method

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10.1016/j.amc.2004.10.055

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title = "PDEPtest: A package for the Painlev{\'e} test of nonlinear partial differential equations",

abstract = "The so-called WTC-Kruskal algorithm is presented in order to study the Painlev{\'e} integrability of nonlinear partial differential equations, which combines the WTC method and Kruskal's simplification method. Based on the WTC, Kruskal and WTC-Kruskal algorithms, we give an implementation in Maple called PDEPtest. This package can handle nonlinear partial differential equations which can be transformed to polynomial ones, and its effectiveness is illustrated by applying it to a variety of equations. Some new results are reported.",

keywords = "Kruskal's simplification, Nonlinear partial differential equations, Painlev{\'e} test, Symbolic computation, The WTC method",

author = "Xu, \{Gui Qiong\} and Li, \{Zhi Bin\}",

year = "2005",

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doi = "10.1016/j.amc.2004.10.055",

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AU - Li, Zhi Bin

PY - 2005/10/15

Y1 - 2005/10/15

N2 - The so-called WTC-Kruskal algorithm is presented in order to study the Painlevé integrability of nonlinear partial differential equations, which combines the WTC method and Kruskal's simplification method. Based on the WTC, Kruskal and WTC-Kruskal algorithms, we give an implementation in Maple called PDEPtest. This package can handle nonlinear partial differential equations which can be transformed to polynomial ones, and its effectiveness is illustrated by applying it to a variety of equations. Some new results are reported.

AB - The so-called WTC-Kruskal algorithm is presented in order to study the Painlevé integrability of nonlinear partial differential equations, which combines the WTC method and Kruskal's simplification method. Based on the WTC, Kruskal and WTC-Kruskal algorithms, we give an implementation in Maple called PDEPtest. This package can handle nonlinear partial differential equations which can be transformed to polynomial ones, and its effectiveness is illustrated by applying it to a variety of equations. Some new results are reported.

KW - Kruskal's simplification

KW - Nonlinear partial differential equations

KW - Painlevé test

KW - Symbolic computation

KW - The WTC method

UR - https://www.scopus.com/pages/publications/25844433033

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DO - 10.1016/j.amc.2004.10.055

M3 - 文章

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EP - 1379

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 2

ER -

PDEPtest: A package for the Painlevé test of nonlinear partial differential equations

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Keywords

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