Superposición de ondas

Clear["Global`*"];
 b[x_] = x*Sin[x] ;  a[x_] = 
      Sin[x];

v[x_, t_] = 
      0.5 (a[x + t]) + 
        0.5 (∫_0^(x + t))b[s] \[DifferentialD]s; 
    w[x_, t_] = 
      0.5 (a[x - t]) - 
        0.5 (∫_0^(x - t))b[s] \[DifferentialD]s

u[x_, t_] = 
      0.5 (a[x + t] + a[x - t]) + 
        0.5 (∫_(x - t)^(x + t))b[
                s] \[DifferentialD]s

Plot[{v[x, 0], w[x, 0], u[x, 0]}, {x, -5, 5}, 
      PlotRange -> {-3.5, 3.5}, 
      PlotStyle -> {{Thickness[0.001]}, {Thickness[0.010]}, {Thickness[
              0.020]}}]

Plot[{v[x, 1], w[x, 1], u[x, 1]}, {x, -5, 5}, 
      PlotRange -> {-3.5, 3.5}, 
      PlotStyle -> {{Thickness[0.001]}, {Thickness[0.010]}, {Thickness[
              0.020]}}]

Plot[{v[x, 2], w[x, 2], u[x, 2]}, {x, -5, 5}, 
      PlotRange -> {-3.5, 3.5}, 
      PlotStyle -> {{Thickness[0.001]}, {Thickness[0.010]}, {Thickness[
              0.020]}}]