A note on duality of first order partial differential equations
type: Item
instance of: scholarly article
title: A note on duality of first order partial differential equations
zbMATH Open document ID: 0831.58052
author: K. Aoki
published in: Hokkaido Mathematical Journal
publication date: 1996-02-22T00:00:00Z
review text: The following generalized Legendre contact transformation of \(J^1 (\mathbb{R}^n, \mathbb{R})\) with the local coordinates \((x, u, p)= (x_1, \dots, x_n, y, p_1, \dots,p_n)\) and \(I\subset \{1, \dots, n\}\), \[ X_{I^c}= x_{I^c}, \quad X_I = p_I, \quad Y= p_I x_I- y, \quad P_{I^c}= p_{I^c}, \quad P_I= x_I \] is used to formulate and prove a duality principle for systems of first order PDE's with complete solutions. A stronger statement is proved for holonomic systems of first order PDE's. These results generalize the earlier work of Izumiya given in the references.
Mathematics Subject Classification ID: 58J70
Mathematics Subject Classification ID: 58J72
Mathematics Subject Classification ID: 35A30
zbMATH DE Number: 784565
zbMATH Keywords: contact transformation
zbMATH Keywords: duality principle
zbMATH Keywords: systems of first order PDE's
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.14492/hokmj/1380892539
OpenAlex ID: W2126856016
DOI: 10.14492/HOKMJ/1380892539
description: scientific article; zbMATH DE number 784565