Abstract
In the present chapter we will consider systems of nonlinear PDEs that are invariant under the Poincare group P(1,3), extended Poincare group \(\tilde P\left( {1,3} \right)\) and conformal group C(1,3). Ansatze for spinor fields will be constructed. The formula of generating solutions (GS) by conformal transformations is obtained for fields of arbitrary spin. Wide classes of exact solutions of nonlinear generalizations of the Dirac equation are found as well as solutions of the quantum electrodynamics nonlinear equations, coupled nonlinear equations for vector and scalar fields, the Yang-Mills equations, and some others.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1993 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Fushchich, W.I., Shtelen, W.M., Serov, N.I. (1993). Systems of Poincare-invariant Nonlinear PDEs. 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_2
Download citation
DOI: https://doi.org/10.1007/978-94-017-3198-0_2
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4244-6
Online ISBN: 978-94-017-3198-0
eBook Packages: Springer Book Archive