  The work extends the linear fields' solution of compressible nonlinear
magnetohydrodynamics~(MHD) to the case where the magnetic field depends on
superlinear powers of position vector, usually but not always, expressed in
Cartesian components. Implications of the resulting Lie-Taylor series expansion
for physical applicability of the Dolzhansky-Kirchhoff~(D-K) equations are
found to be positive. It is demonstrated how resistivity may be included in the
D-K model. Arguments are put forward that the D-K equations may be regarded as
illustrating properties of nonlinear MHD in the same sense that the Lorenz
equations inform about the onset of convective turbulence. It is suggested that
the Lie-Taylor series approach may lead to valuable insights into other fluid
models.
