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

  • N. Euler
  • P. G. L. Leach
  • F. M. Mahomed
  • W. -H. Steeb
Article

Abstract

In the study of the formulation of Maxwellian tails the nonlinear partial differential equation2u/∂x ∂τ+∂u/∂x+u2=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.

Keywords

Differential Equation Field Theory Elementary Particle Partial Differential Equation Quantum Field Theory 

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References

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Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • N. Euler
    • 1
  • P. G. L. Leach
    • 2
    • 3
  • F. M. Mahomed
    • 2
  • W. -H. Steeb
    • 1
    • 3
  1. 1.Department of PhysicsRand Afrikaans UniversityJohannesburgSouth Africa
  2. 2.Department of Computational and Applied MathematicsUniversity of the WitwatersrandJohannesburgSouth Africa
  3. 3.Centre for Nonlinear StudiesUniversity of the WitwatersrandJohannesburgSouth Africa

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