On the reduction of some systems of partial differential equations to first order systems with only one unknown function

  1. S. Jiménez 1
  2. J. Muñoz 1
  3. J. Rodríguez 1
  1. 1 Departamento de Matemáticas, Univ. de Salamanca
Book:
Differential geometry and its applications : proceedings
  1. Oldřich Kowalski (ed. lit.)
  2. Demeter Krupka (ed. lit.)
  3. Jan Slovák (ed. lit.)

Publisher: Silesian University at Opava

ISBN: 8072481665

Year of publication: 2001

Pages: 187-195

Type: Book chapter

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Abstract

Inspired in part by some ideas of Lie, we define canonical correspondences between jet spaces which, when specialized to a system of partial differential equations, under certain conditions allow one to transform a given system into a first order one with only one unknown function. To illustrate the general theory, we describe the results that can be obtained for a class of second order systems, thus clarifying and completing some partial results of Lie.