jet[u_?NumericQ] :=
Blend[{{0, RGBColor[0, 0, 9/16]}, {1/9, Blue}, {23/63, Cyan}, {13/21,
Yellow}, {47/63, Orange}, {55/63, Red}, {1,
RGBColor[1/2, 0, 0]}}, u] /; 0 <= u <= 1
Usage example:
Plot3D[Abs[u1[x,t]], {x, -5, 5}, {t, -3, 3}, PlotRange -> All,
PlotPoints -> 100, AxesLabel -> {"x", "t", "|u1|"},
ColorFunction -> jet, Mesh -> None]