V[x_] := 1 - Cos[x];
s1 = NDSolve[{D[u[x], x] == Sqrt[2 V[u[x]]], u[0] == Pi}, u, {x, -20, 20}]
f11=Plot3D[V[u],{x,-10,10},{u,-Pi,3 Pi}];
u1[x_]:=u[x]/.s1;
f12=ParametricPlot3D[{x,u1[x],V[u1[x]]},{x,-10,10},PlotRange->{-10,10},BoxRatios->{10,20,10},PlotStyle->{Black,Thick}];

Show[f11,f12]

V[x_] :=1/2 (x^2-1)^2;
s2 = NDSolve[{D[u[x], x] == Sqrt[2 V[u[x]]], u[0] == 0}, u, {x, -20, 20}]
f21=Plot3D[V[u],{x,-10,10},{u,-1.5,1.5}];
u2[x_]:=u[x]/.s2;
f22=ParametricPlot3D[{x,u2[x],V[u2[x]]},{x,-10,10},PlotRange->{-10,10},BoxRatios->{10,20,10},PlotStyle->{Black,Thick}];

Show[f21,f22]

V2[x_] :=1/2 x^2 (x^2-1)^2;
s4 = NDSolve[{D[u[x], x] == Sqrt[2 V2[u[x]]], u[0] == -0.1}, u, {x, -10, 10}]
f41=Plot3D[V2[u],{x,-10,10},{u,-1.2,1.2}];
u4[x_]:=u[x]/.s4;
f42=ParametricPlot3D[{x,u4[x],V2[u4[x]]},{x,-10,10},PlotRange->{-10,10},BoxRatios->{10,20,10},PlotStyle->{Black,Thick}];

Show[f41,f42]

V[x_]:=1/2 (x^2-1)^2 (x^2-9)^2;
s31 = NDSolve[{D[u[x], x] == Sqrt[2 V[u[x]]], u[0] == 0}, u, {x, -10, 10}]
s32 = NDSolve[{D[u[x], x] == Sqrt[2 V[u[x]]], u[0] == 1.5}, u, {x, -10, 10}]
f31=Plot3D[V[u],{x,-1,1},{u,-3.3,3.5}];
u31[x_]:=u[x]/.s31;
u32[x_]:=u[x]/.s32;
f32=ParametricPlot3D[{x,u31[x],V[u31[x]]},{x,-1,1},PlotRange->{-10,10},BoxRatios->{10,20,10},PlotStyle->{Black,Thick}];
f33=ParametricPlot3D[{x,u32[x],V[u32[x]]},{x,-1,1},PlotRange->{-10,10},BoxRatios->{10,20,10},PlotStyle->{Red,Thick}];

Show[f31,f32,f33]