Igor SHIROKOV
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

Abstract:
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.