PainleveBacklundCheck: A Sympy-powered Kivy app for the Painlevé property of nonlinear dispersive PDEs and auto-Bäcklund transformations

In the present work we revisit the Painlevé property for partial differential equations. We consider the PDE variant of the relevant algorithm on the basis of the fundamental work of Weiss, Tabor and Carnevale and explore a number of relevant examples. Subsequently, we present an implementation of t...

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Bibliographic Details
Published in:arXiv.org 2024-03
Main Authors: Mohapatra, Shrohan, Kevrekidis, P G, Lafortune, Stephane
Format: Article
Language:English
Subjects:
Algorithms
Partial differential equations
Online Access:Get full text
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Summary:In the present work we revisit the Painlevé property for partial differential equations. We consider the PDE variant of the relevant algorithm on the basis of the fundamental work of Weiss, Tabor and Carnevale and explore a number of relevant examples. Subsequently, we present an implementation of the relevant algorithm in an open-source platform in Python and discuss the details of a Sympy-powered Kivy app that enables checking of the property and the derivation of associated auto-B{\"a}ck{u}nd transform when the property is present. Examples of the relevant code and its implementation are also provided, as well as details of its open access for interested potential users.
ISSN:2331-8422