window[x_] := (Cos[Pi x] + 1)/2;
n = 3;
ps = {0.6, -0.3, 0.1};
as = {0.1, 0.5, 0.8};
initu[x_] := Sum[2 as[[i]] Exp[-20 (x - ps[[i]])^2], {i, n}];
Tmax = 80;
\[Tau] = 0.1; du2 = 0.00028; dv2 = 0.005; \[Kappa] = -0.005;
soln = NDSolve[{
D[u[x, t], t] ==
du2 D[u[x, t], {x, 2}] + u[x, t] - u[x, t]^3 -
v[x, t] - \[Kappa],
\[Tau] D[v[x, t], t] ==
dv2 D[v[x, t], {x, 2}] + u[x, t] - v[x, t],
u[x, 0] == 0.5 window[x] x,
v[x, 0] == 0.1 window[x],
Derivative[1, 0][u][-1, t] == 0,
Derivative[1, 0][u][1, t] == 0,
Derivative[1, 0][v][-1, t] == 0,
Derivative[1, 0][v][1, t] == 0
}, {u, v}, {x, -1, 1}, {t, 0, Tmax}];
frame[tt_] := Show[
ArrayPlot[{
Table[
Tanh[
3 Max[0, (First[(u[x, t] - v[x, t]) /. soln] /. {x -> xx,
t -> tt})]]^2,
{xx, -1, 1, 2/100}]}
, AspectRatio -> 1, ColorFunction -> "DeepSeaColors",
Frame -> False]
,
Plot[
Max[0, (1 + First[(u[x, t] /. soln)] /. {x -> (xx - 50)/50,
t -> tt})/2]
, {xx, 0, 101}, PlotRange -> {-1, 1},
PlotStyle -> Directive[Thick, Red], Axes -> None],
Plot[
Max[0, (1 + First[(v[x, t] /. soln)] /. {x -> (xx - 50)/50,
t -> tt})/2]
, {xx, 0, 101}, PlotRange -> {-1, 1},
PlotStyle -> Directive[Thick, Yellow]],
ImageSize -> 300];
Manipulate[
frame[Exp[tt] - 0.99],
{tt, 0, 3.5}
]