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Open Access Case study

Geometry of distributions and F-Gordon equation

Mehdi Nadjafikhah1 and Reza Aghayan2*

Author Affiliations

1 Faculty of Mathematics, School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, 16846-13114, Iran

2 Department of Basic Sciences, Eslamshahr Branch, Islamic Azad University, Eslamshahr, 3314853186, Iran

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Mathematical Sciences 2012, 6:49  doi:10.1186/2251-7456-6-49

Published: 9 October 2012

Abstract

In this paper, we describe the geometry of distributions by their symmetries and present a simplified proof of the Frobenius theorem and some related corollaries. Then, we study the geometry of solutions of the F-Gordon equation, a PDE which appears in differential geometry and relativistic field theory.

Keywords:
Distribution; Lie symmetry; Contact geometry; Klein-Gordon equation