  The Theory of (2+1) Systems based on 2D Schrodinger Operator was started by
S.Manakov, B.Dubrovin, I.Krichever and S.Novikov in 1976. The Analog of Lax
Pairs introduced by Manakov, has a form $L_t=[L,H]-fL$ ("The $L,H,f$-triples")
where $L=\partial_x\partial_y+G\partial_y+S$ and $H,f$-some linear PDEs. Their
Algebro-Geometric Solutions and therefore the full higher order hierarchies
were constructed by B.Dubrovin, I.Krichever and S.Novikov. The Theory of 2D
Inverse Spectral Problems for the Elliptic Operator $L$ with $x,y$ replaced by
$z,\bar{z}$, was started by B.Dubrovin, I.Krichever and S.Novikov: The Inverse
Spectral Problem Data are taken from the complex "Fermi-Curve" consisting of
all Bloch-Floquet Eigenfunctions $L\psi=const$. Many interesting systems were
found later. However, specific properties of the very first system, offered by
Manakov for the verification of new method only, were not studied more than 10
years until B.Konopelchenko found in 1988 analogs of Backund Transformations
for it. He pointed out on the "Burgers-Type Reduction". Indeed, the present
authors quite recently found very interesting extensions, reductions and
applications of that system both in the theory of nonlinear evolution systems
(The Self-Adjoint and 2D Burgers Hierarhies were invented, and corresponding
reductions of Inverse Problem Data found) and in the Spectral Theory of
Important Physical Operators ("The Purely Magnetic 2D Pauli Operators"). We
call this system GKMMN by the names of authors who studied it.
