  Different definitions of integrability, as a rule, use linearization of
initial equation and/or expansion on some basic functions which are themselves
solutions of some linear differential equation. Important fact here is that
linearization of some differential equation is its simplification but not
solving yet. For instance, in case of linear Schroedinger equation, we are not
able to find its solutions explicitly but only to name them Jost functions and
to exploit their useful properties (see previous Chapters).
  On the other hand, well-known fact is that for LODE with constant
coefficients operator itself can always be factorized into first-order factors
and thus the problem is reduced to the solving of a few first-order LODEs which
are solvable in quadratures.
  In case of differential operators with variable coefficients factorization is
not always possible but for the great number of operators BK-factorization
gives factorization conditions explicitly which we are going to demonstrate in
this Chapter. BK factorization is used to construct set of invariants for LPDO
of arbitrary order; interconnections of these new invariants with classic
Laplace invariants for second order hyperbolic LPDOs are discussed.
