The pole dynamics of rational solutions of the viscous Burgers equation

Rational solutions of the viscous Burgers equation are examined using the dynamics of their poles in the complex x-plane. The dynamical system for the motion of these poles is finite dimensional and not Hamiltonian. Nevertheless, we show that this finite-dimensional system is completely integrable, by explicit construction of a sufficient number of conserved quantities. The dynamical system has a class of non-equilibrium similarity solutions for which all poles have equal real part for t sufficiently large. Within the context of the finite-dimensional dynamical system these solutions are shown to be asymptotically stable.