Compressible Helical Beltrami Flow
Consider the case of a compressible fluid undergoing helical (Beltrami) flow with nonuniform vorticity and velocity. This is a generalization of the ABC (Arnold–Beltrami–Childress) flow for the compressible case  in which chaotic dynamics appear  that involve a "Q-flow" (flows with quasisymmetry).
The Q-flows have a Hamiltonian ; then
where is a perturbation parameter (when the advection equations are integrable) and
with and .
Now, introducing a soliton-like function related to the Beltrami flow condition for a scalar function (condition for compressibility), in this case of the form
where the variable is used instead of and are related according to , is a constant, and is a scale parameter along . Consider a generating function of the type
then, rewriting the equations, we have
 A. Morgulis, V. I. Yudovich, and G. M. Zaslavsky, "Compressible Helical Flows," Communications on Pure and Applied Mathematics, 48(5), 2006 pp. 571–582. doi:10.1002/cpa.3160480505
 G. M. Zaslavsky, Hamiltonian Chaos and Fractional Dynamics, New York: Oxford University Press, 2005.