An exact nonlinear mode of a coupled advection equation in a volume-preserving system

Abstract

We investigate an exact solution of a nonlinear coupled advection equation in a volume-preserving system. The Hamiltonian of the system is obtained by reinterpreting a Poincaré invariant as the Hamiltonian. Hamilton’s equations of motion yield a nonlinear coupled advection equation. We also discuss properties of the nonlinear coupled advection equation related to the exact solution, including constants of motion.