Clear["Global`*"]
numberpics = 50;
step = 5;
numberpoints = 100;

 (* (Subscript[J, n])(z)satisfies the differential equation(z^2) (y^′)′ + 
                z  (y^′) + ((z^2) - (n^2)) y = 0 *)
Table[Plot3D[BesselJ[0,  Sqrt[(x^2)+(y^2)]-tt/10] Exp[-0 tt/numberpics] ,{x, -10, 10},{y, -10, 10},Axes -> False,Boxed -> False,Mesh -> False,PlotPoints -> numberpoints,PlotRange -> {{-10, 10}, {-10, 
                    10}, {-1, 1}},PlotRegion -> Automatic],{tt, 0, numberpics, step}];

(* The Legendre polynomials satisfy the differential equation(1 - (x^2)) ((d^2) y/d  (x^2)) - 
                2  x(d  y/d  x) + n(n + 1) y = 0 *)

numberpics = 
          50;
step = 
        5;
numberpoints = 
        100;
Table[Plot3D[LegendreP[2,  Sqrt[(x^2)+(y^2)]-tt/25] Exp[-0 tt/numberpics] ,{x, -1, 1},{y, -1, 1},Axes -> False,Boxed -> False,Mesh -> False,PlotPoints -> numberpoints,PlotRange -> {{-1, 1}, {-1, 1}, {0, 5}},PlotRegion -> Automatic],{tt, 0, numberpics, step}];