  In the high energy limit, soft gluons can be approximately described by
quasi-classical gluon fields. It is well-known that the gluon field is a pure
gauge field on the transverse plane at eikonal order. We derived the complete
next-to-eikonal order solutions of the classical Yang-Mills equations for soft
gluons in the dense nuclear regime. Utilizing these solutions, it is shown that
Low's soft theorem at small x can be obtained by considering off-diagonal
matrix elements of quasi-classical chromoelectric field between single gluon
states in the dilute regime. We further propose on extending Low's soft theorem
at small x to incorporate the effects of gluon saturation in the dense regime.
