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Poincare-Invariant Nonlinear Scalar Equations

  • W. I. Fushchich
  • W. M. Shtelen
  • N. I. Serov
Chapter
Part of the Mathematics and Its Applications book series (MAIA, volume 246)

Abstract

In the present chapter we describe the first- and second-order n-dimensional nonlinear PDEs which are invariant under the groups \(\widetilde P\left( {1,1 - n} \right),\widetilde P\left( {1,n} \right)\) . We investigate local and tangent symmetry of the relativistic Hamilton equation, of the nonlinear d’Alembert equation, of the Euler-Lagrange-Born-Infeld equation, the Monge-Ampere equation, and some other PDEs. For this purpose the Lie method has been used with the exception of Sec. 1.3, where the symmetry of the polywave equation is investigated by the operator method expounded in Sec. 5.5.

Keywords

Arbitrary Constant Invariance Condition Nonlinear Wave Equation Conformal Group Contact Transformation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  • W. I. Fushchich
    • 1
  • W. M. Shtelen
    • 1
  • N. I. Serov
    • 1
  1. 1.Institute of MathematicsKievUkraine

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