The Euler Equations of Spatial Gasdynamics and the Integrable Heisenberg Spin Equation

摘要

The Euler equations for an inviscid and thermally nonconducting gas are investigated with a view to isolating particular integrable structure. A natural physical constraint is imposed and it is demonstrated that, in the generic case, the steady Euler equations are equivalent to an integrable Heisenberg spin equation subject to a volume-preserving constraint. A limiting case in which this constraint is not present is indicated.