Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple

Gui Qiong Xu; Zhi Bin Li

doi:10.1016/j.cpc.2004.04.005

Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple

Gui Qiong Xu^*
, Zhi Bin Li

^*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

73 引用（Scopus）

摘要

A software package wkptest written in Maple is presented, which can carry out the traditional Painlevé test for polynomial partial differential equations automatically. Furthermore, some truncated expansions are also obtained whether an equation passes the test or not. The truncated expansions play an important role in studying the integrability, such as Lax pairs, bilinear forms, Darboux transformations and explicit solutions. The effectiveness of wkptest is illustrated by applying it to a variety of equations.

源语言	英语
页（从-至）	65-75
页数	11
期刊	Computer Physics Communications
卷	161
期	1-2
DOI	https://doi.org/10.1016/j.cpc.2004.04.005
出版状态	已出版 - 1 8月 2004

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title = "Symbolic computation of the Painlev{\'e} test for nonlinear partial differential equations using Maple",

abstract = "A software package wkptest written in Maple is presented, which can carry out the traditional Painlev{\'e} test for polynomial partial differential equations automatically. Furthermore, some truncated expansions are also obtained whether an equation passes the test or not. The truncated expansions play an important role in studying the integrability, such as Lax pairs, bilinear forms, Darboux transformations and explicit solutions. The effectiveness of wkptest is illustrated by applying it to a variety of equations.",

keywords = "Nonlinear partial differential equations, Painlev{\'e} test, Symbolic computation, Truncated expansion",

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year = "2004",

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N2 - A software package wkptest written in Maple is presented, which can carry out the traditional Painlevé test for polynomial partial differential equations automatically. Furthermore, some truncated expansions are also obtained whether an equation passes the test or not. The truncated expansions play an important role in studying the integrability, such as Lax pairs, bilinear forms, Darboux transformations and explicit solutions. The effectiveness of wkptest is illustrated by applying it to a variety of equations.

AB - A software package wkptest written in Maple is presented, which can carry out the traditional Painlevé test for polynomial partial differential equations automatically. Furthermore, some truncated expansions are also obtained whether an equation passes the test or not. The truncated expansions play an important role in studying the integrability, such as Lax pairs, bilinear forms, Darboux transformations and explicit solutions. The effectiveness of wkptest is illustrated by applying it to a variety of equations.

KW - Nonlinear partial differential equations

KW - Painlevé test

KW - Symbolic computation

KW - Truncated expansion

UR - https://www.scopus.com/pages/publications/3042711333

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VL - 161

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JO - Computer Physics Communications

JF - Computer Physics Communications

IS - 1-2

ER -

Symbolic computation of the Painlevé test for nonlinear partial differential equations using Maple

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