  In this work the construction of supergravity duals to the noncommutative
${\cal N}=4$ SYM theory in the infinite momentum frame but with constant
momentum density is attempted. In the absence of the content of
noncommutativity, it has been known for some time that the previous
$AdS_{5}/CFT_{4}$ correspondence should be replaced by the $K_{5}/CFT_{4}$
(with $K_{(p+2)}$ denoting the generalized Kaigorodov spacetime) correspondence
with the pp-wave propagating on the BPS brane worldvolume. Interestingly
enough, putting together the two contents, i.e., the introduction of
noncommutativity and at the same time that of the pp-wave along the brane
worldvolume, leads to quite nontrivial consequences such as the emergence of
``time-space'' noncommutativity in addition to the ``space-space''
noncommutativity in the manifold on which the dual gauge theory is defined.
Taking the gravity decoupling limit, it has been realized that for small $u$,
the solutions all reduce to $K_{5}\times S^5$ geometry confirming our
expectation that the IR dynamics of the dual gauge theory should be unaffected
by the noncommutativity while as $u\to \infty$, the solutions start to deviate
significantly from $K_{5}\times S^5$ limit indicating that the UV dynamics of
the dual gauge theory would be heavily distorted by the effect of
noncommutativity.
