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

Research output: Contribution to Journal/MagazineJournal articlepeer-review

<mark>Journal publication date</mark>1/01/1995
<mark>Journal</mark>Journal of Differential Equations
Issue number1
Number of pages13
Pages (from-to)153-165
Publication StatusPublished
<mark>Original language</mark>English


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.