Improved Hydrodynamic Theory of Surface Plasmons

We show that there exists a "hydrodynamic" solution of the Boltzmann equation for surface plasmons outside the selvage region of the form $n_1=e^{-\lambda z}$. We determine $\lambda$, find the dispersion relation for the step-density model, discuss the relationship between the hydrodynamic and general solutions of the Boltzmann equation, and suggest a slight modification of the usual hydrodynamic equation to make it compatible with the hydrodynamic solution of the Boltzmann equation.