Bifurcations of completely integrable 2-variable first-order partial differential equations
type: Item
instance of: scholarly article
title: Bifurcations of completely integrable 2-variable first-order partial differential equations
zbMATH Open document ID: 1254.35020
author: Liang Chen
author: Jingbo Xu
author: Weizhi Sun
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-06-20T00:00:00Z
review text: The authors consider an implicit 2-variable first-order partial differential equations \[ F(x_{1}, x_{2}, y, \frac{dy}{dx_{1}}, \frac{dy}{dx_{2}})=0, \] where \(F\) is a sufficiently smooth function and \(0\) is its regular value, i.e., \(F^{-1}(0)\) is a \(3D\) submanifold of \(J^{1}(\mathbb{R}^{2},\mathbb{R})\) (1-jet bundle of 2-variable function). By using Legendrian singularity theory, here, the generic classification is given for bifurcations of such differential equations with respect to the equivalence relation determined by the Lie group of point transformations.
reviewed by: Svetlana A. Grishina
Mathematics Subject Classification ID: 35B32
Mathematics Subject Classification ID: 35F20
Mathematics Subject Classification ID: 35A20
Mathematics Subject Classification ID: 58K70
zbMATH DE Number: 5909845
zbMATH Keywords: Legendrian singularity
zbMATH Keywords: complete integral
zbMATH Keywords: generic classification
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.03.020
OpenAlex ID: W2087272082
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DOI: 10.1016/J.JMAA.2011.03.020
description: scientific article; zbMATH DE number 5909845