  The dynamics of many natural systems is dominated by non-linear waves
propagating through the medium. We show that the dynamics of non-linear wave
fronts with positive surface tension can be formulated as a gradient system.
The variational potential is simply given by a linear combination of the
occupied volume and surface area of the wave front, and changes monotonically
in time. Finally, we demonstrate that vortex filaments can be written as a
gradient system only if their binormal velocity component vanishes, which
occurs in chemical system with equal diffusion of reactants.
