  The present paper suggests the continuum theory of Tkachenko modes in a
rotating 2D Bose-Einstein condensate taking into account density inhomogeneity
and compressibility of the condensate. The problem requires solution of coupled
hydrodynamic equations for vortex and liquid motion with proper boundary
conditions, which were derived for the condensate described by the Thomas-Fermi
approximation. Compressibility becomes essential at rapid rotation with angular
velocity close to the trap frequency. The theory is in a reasonable agreement
with experimental observation of Tkachenko modes.
