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Travelling wave solutions to some PDE s of mathematical physics

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  • Kourosh Nozari
  • Ghasem Alizadeh Afrouzi

Abstract

Nonlinear operations such as multiplication of distributions are not allowed in the classical theory of distributions. As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space-times. Colombeau's new theory of generalized functions can be used to remove these ambiguities. In this paper, we first consider a simplified model of elasticity and multifluid flows in the framework of Colombeau's theory and show how one can handle such problems, investigate their jump conditions, and resolve their ambiguities. Then we consider as a new proposal the case of cosmological models with signature change and use Colombeau's theory to solve Einstein equation for the beginning of the Universe.

Suggested Citation

  • Kourosh Nozari & Ghasem Alizadeh Afrouzi, 2004. "Travelling wave solutions to some PDE s of mathematical physics," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-16, January.
    • Handle: RePEc:hin:jijmms:519790
    DOI: 10.1155/S0161171204108028
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    Cited by:

    1. Nozari, Kourosh, 2006. "Nonlinear operations on distributions and application to cosmology of very early universe," Chaos, Solitons & Fractals, Elsevier, vol. 30(2), pages 290-299.

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