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

^*Corresponding author for this work

School of Mathematical Sciences

East China Normal University
Shanghai University

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

73 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	65-75
Number of pages	11
Journal	Computer Physics Communications
Volume	161
Issue number	1-2
DOIs	https://doi.org/10.1016/j.cpc.2004.04.005
State	Published - 1 Aug 2004

Keywords

Nonlinear partial differential equations
Painlevé test
Symbolic computation
Truncated expansion

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10.1016/j.cpc.2004.04.005

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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

U2 - 10.1016/j.cpc.2004.04.005

DO - 10.1016/j.cpc.2004.04.005

M3 - 文章

AN - SCOPUS:3042711333

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VL - 161

SP - 65

EP - 75

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

Abstract

Keywords

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