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

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 v...

Title of program: wkptest
Catalogue Id: ADTY_v1_0

Nature of problem
Our program can perform the traditional Painlevé test for nonlinear partial differential equations automatically, and some truncated expansions are also obtained whether or not the given equations pass the test. The obtained truncated expansions play an important role in studying the integrability as well as constructing explicit exact solutions.

Versions of this program held in the CPC repository in Mendeley Data
ADTY_v1_0; wkptest; 10.1016/j.cpc.2004.04.005

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2018)

本文提出了一种以 Maple 语言编写的软件包 wkptest，该软件包能够自动执行多项式偏微分方程的传统 Painlevé 测试。此外，无论方程是否通过测试，还获得了截断展开式。这些截断展开式在研究可积性（例如，Lax 对、双线性形式、Darboux 变换和显式解）方面发挥着至关重要的作用。通过将该程序应用于示例，展示了 wkptest 的有效性。程序名称：wkptest
目录编号：ADTY_v1_0
问题性质：我们的程序能够自动执行非线性偏微分方程的传统 Painlevé 测试，并且无论给定方程是否通过测试，还会获得一些截断展开式。这些获得的截断展开式在研究可积性以及构建显式精确解方面发挥着至关重要的作用。
Mendeley 数据库中 CPC 存储库中保存的此程序的版本：ADTY_v1_0; wkptest; 10.1016/j.cpc.2004.04.005
此程序已从贝尔法斯特女王大学（1969-2018年）保存的 CPC 程序库中导入。