10.1186/2251-7456-6-49

Geometry of distributions and F-Gordon equation

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  • Mehdi Nadjafikhah1,
  • Reza Aghayan*2,
  1. Faculty of Mathematics, School of Mathematics, Iran University of Science and Technology, Tehran, Narmak, 16846-13114, IR
  2. Department of Basic Sciences, Eslamshahr Branch, Islamic Azad University, Eslamshahr, 3314853186, IR

Published in Issue 2012-10-09

How to Cite

Nadjafikhah, M., & Aghayan, R. (2012). Geometry of distributions and F-Gordon equation. Mathematical Sciences, 6(1). https://doi.org/10.1186/2251-7456-6-49
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Abstract

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
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References

  1. Barone et al. (1971) Theory and applications of the Sine-Gordon equation (pp. 227-267) https://doi.org/10.1007/BF02820622
  2. Kragh (1984) Equation with the many fathers. The Klein-Gordon equation in 1926 52(11) (pp. 1024-1033) https://doi.org/10.1119/1.13782
  3. Alekseevskij et al. (1991) Springer
  4. Kushner et al. (2007) Cambridge University Press