An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics

Fackerell, E. D. and Hartley, D. H. and Tucker, Robin (1995) An obstruction to the integrability of a class of non-linear wave equations by 1-stable cartan characteristics. Journal of Differential Equations, 115 (1). pp. 153-165. ISSN 0022-0396

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Abstract

We examine in detail the Cauchy problem for a class of non-linear hyperbolic equations in two independent variables. This class is motivated by the analysis of the dynamics of a line of non-linearly coupled particles by Fermi, Pasta, and Ulam and extends the recent investigation of this problem by Gardner and Kamran. We find conditions for the existence of a 1-stable Cartan characteristic of a Pfaffian exterior differential system whose integral curves provide a solution to the Cauchy problem. The same obstruction to involution is exposed in Darboux′s method of integration and the two approaches are compared. A class of particular solutions to the obstruction is constructed.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Differential Equations
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2603
Subjects:
ID Code:
75062
Deposited By:
Deposited On:
07 Aug 2015 11:16
Refereed?:
Yes
Published?:
Published
Last Modified:
01 Jan 2020 09:19