A constructive REDUCE package based upon the Painlevé analysis of nonlinear evolutions equations in Hamiltonian and / or normal form

Abstract
A number of necessary conditions for scalar nonlinear evolution equations of normal or certain Hamiltonian form to pass the Painlevé test in one (or two) branches with the Kruskal ansatz is used to write a REDUCE package able to construct (theoretically) all equations with this property. Starting with a given leading order, a degree of homogeneity and (in the Hamiltonian case) a skew-adjoint differential operator, the system generates all admissible resonance patterns, adapts (if possible) th...

Title of program: PTEST.RED
Catalogue Id: ACHP_v1_0

Nature of problem
To find physically good natured nonlinear evolution equations passing the Painleve test and exhibiting e.g. soliton solutions, Baecklund transformations, an infinite number of conserved densities and/or symmetries.

Versions of this program held in the CPC repository in Mendeley Data
ACHP_v1_0; PTEST.RED; 10.1016/0010-4655(92)90203-B

This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)

摘要：本文基于标量非线性演化方程在正常形式或特定哈密顿形式下通过 Painlevé 测试的必要条件，利用 Kruskal 构型，构建了一个 REDUCE 软件包。该软件包能够（理论上）构造出所有具备此性质的方程。从给定的一阶主导项、齐次度以及（在哈密顿情形下）斜对称微分算子出发，该系统可生成所有容许的共振模式，并在可能的情况下进行自适应调整……

程序名称：PTEST.RED
目录编号：ACHP_v1_0

问题性质：寻找具有良好物理性质的非线性演化方程，这些方程通过 Painlevé 测试，并展现出例如孤子解、Baecklund 变换、无限多个守恒密度以及/或对称性。

本程序版本存放在 Mendeley 数据库中 CPC 存储库：ACHP_v1_0; PTEST.RED; 10.1016/0010-4655(92)90203-B

此程序已从贝尔法斯特女王大学（1969-2019年）的 CPC 程序库中导入。