It is well-known that solitary waves on shallow water can be modeled by nonlinear KdV and nonlinear Schrodinger (NLS) equations. These equations may be deduced from the operator Lax equation Ablowitz-Kaup-Newel-Segur proposed to use the matrix version of Lax equation to produce solvable nonlinear equation. This presentation gives the extension of the Lax equation on a time-space scale. Using this extension, we deduce NLS on a space scale.