We investigate the breathing of optical spatial solitons in highly nonlocal
media. Generalizing the Ehrenfest theorem, we demonstrate that oscillations in
beam width obey a fourth-order ordinary differential equation. Moreover, in
actual highly nonlocal materials, the original accessible soliton model by
Snyder and Mitchell [Science \textbf{276}, 1538 (1997)] cannot accurately
describe the dynamics of self-confined beams as the transverse size
oscillations have a period which not only depends on power but also on the
initial width. Modeling the nonlinear response by a Poisson equation driven by
the beam intensity we verify the theoretical results against numerical
simulations.Comment: 7 pages, 4 figures, resubmitted to Physical Review
