Symmetry Analysis and Exact Solutions of Equations of Nonlinear Mathematical Physics pp 55-146 | Cite as

# Systems of Poincare-invariant Nonlinear PDEs

## 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.

## Keywords

Dirac Equation Arbitrary Constant Conformal Transformation Spinor Field Poincare Group## Preview

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