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.
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© 1993 Springer Science+Business Media Dordrecht
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Fushchich, W.I., Shtelen, W.M., Serov, N.I. (1993). Poincare-Invariant Nonlinear Scalar Equations. In: Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics. Mathematics and Its Applications, vol 246. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-3198-0_1
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DOI: https://doi.org/10.1007/978-94-017-3198-0_1
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4244-6
Online ISBN: 978-94-017-3198-0
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