m=1
q=5/2
K = Sqrt[4 m/(3 - q)]
ξ = (q - 1)^2/4 K^2
A = Pi/Sqrt[ξ]
Plot3D[1/A (1 + (q - 1) (Sqrt[ξ]) (x t))/(1 + ξ x^2), {x, 0, 20}, {t,
0, 5000}, PlotLabel -> "q=5/4", BaseStyle -> {FontSize -> 20},
AxesLabel -> {Framed["x", FrameStyle -> None, FrameMargins -> 25],
Framed["t", FrameStyle -> None, FrameMargins -> 25],
Framed["ρ(x,t)", FrameStyle -> None, FrameMargins -> 25]},
LabelStyle -> Directive[16]]