  For the noncommutative torus ${\cal T}$, in case of the N.C. parameter
$\theta = \frac{Z}{n}$, we construct the basis of Hilbert space ${\ca$H}_n$ in
terms of $\theta$ functions of the positions $z_i$ of $n$ solitons. The
wrapping around the torus generates the algebra ${\cal A}_n$, which is the $Z_n
\times Z_n$ Heisenberg group on $\theta$ functions. We find the generators $g$
of an local elliptic $su(n)$, w$transform covariantly by the global gauge
transformation of ${\cal A}$By acting on ${\cal H}_n$ we establish the
isomorphism of ${\cal A}_n$$g$. We embed this $g$ into the $L$-matrix of the
elliptic Gaudin and$models to give the dynamics. The moment map of this twisted
cotangent $su_n({\cal T})$ bundle is matched to the $D$-equation with
Fayet-Illiopoulos source term, so the dynamics of the N.C. solitons becomes
that of the brane. The geometric configuration $(k, u)$ of th$spectral curve
${\rm det}|L(u) - k| = 0$ describes the brane configuration, with the dynamical
variables $z_i$ of N.C. solitons as$moduli $T^{\otimes n} / S_n$. Furthermore,
in the N.C. Chern-Simons theory for the quantum Hall effect, the constrain
equation with quasiparticle source is identified also with the moment map
eqaution $the N.C. $su_n({\cal T})$ cotangent bundle with marked points. The
eigenfunction of the Gaudin differential $L$-operators as the
Laughli$wavefunction is solved by Bethe ansatz.
