IJPAM: Volume 48, No. 3 (2008)

ON THE EXISTENCE OF ANALYTIC SOLUTIONS
OF THE D'ALEMBERT EQUATION

Zbigniew Lesniak
Institute of Mathematics
Pedagogical University
2, Podchorazych, Kraków, 30-084, POLAND
e-mail: zlesniak@ap.krakow.pl


Abstract.We study the d'Alembert partial differential equation as a submanifold of the jet space $J^2(\mathbb{R}^2,\mathbb{R})$ with the contact system defined on it. We prove the existence of analytic solutions of this equation by using the Cartan-Kähler Theorem. These solutions are parametrized by two arbitrary analytic functions of one variable.

Received: August 26, 2008

AMS Subject Classification: 35A30, 35L25, 35C05

Key Words and Phrases: partial differential equation, exterior differential system, Pfaffian system, Cartan-Kähler Theorem.

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 48
Issue: 3