Physics Department, Omsk State University,
55-a Mira Ave., Omsk,  644077, RUSSIA
E-mail: shirokov@univer.omsk.su

Application of the orbits method for integration of the linear PDE with noncommutative symmetry group

Invariant linear PDE's on homogeneous spaces are considered. Equation on homogeneous space is reduced to the equation on Lagrange submanifold to the coadjoint orbit. As a result sufficient and necessary conditions of integrability for the equations of that class are obtained.