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Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution

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Abstract

In the study of the formulation of Maxwellian tails the nonlinear partial differential equation∂ 2 u/∂x ∂τ+∂u/∂x+u 2=0 arises. We determine the Lie point symmetry vector fields and calculate the similarity ansätze. Then we discuss the resulting ordinary differential equations. Finally, the existence of Lie Bäcklund vector fields is studied and a Painlevé analysis is performed.

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Authors and Affiliations

  1. Department of Physics, Rand Afrikaans University, 2000, Johannesburg, South Africa

    N. Euler & W. -H. Steeb

  2. Department of Computational and Applied Mathematics, University of the Witwatersrand, 2001, Johannesburg, South Africa

    P. G. L. Leach & F. M. Mahomed

  3. Centre for Nonlinear Studies, University of the Witwatersrand, 2001, Johannesburg, South Africa

    P. G. L. Leach & W. -H. Steeb

Authors
  1. N. Euler
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  2. P. G. L. Leach
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  3. F. M. Mahomed
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  4. W. -H. Steeb
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Euler, N., Leach, P.G.L., Mahomed, F.M. et al. Symmetry vector fields and similarity solutions of a nonlinear field equation describing the relaxation to a maxwell distribution. Int J Theor Phys 27, 717–723 (1988). https://doi.org/10.1007/BF00669316

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  • DOI: https://doi.org/10.1007/BF00669316

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