Wolfram Technology Guide: Dynamic Interactivity  previous | next 
Interactively Explore New Frontiers
Mathematica makes it possible to explore new phenomena by direct interactive exploration--here a space of nonlinear PDEs.
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Click for copyable input
Manipulate[

 Plot3D[Evaluate[

   u[t, x] /. 

    Quiet[NDSolve[

      Evaluate[{D[u[t, x], t, t] == 

         D[u[t, x], x, x] + a u[t, x]^3 + b u[t, x]^2 + c u[t, x] + d,

         u[0, x] == \[ExponentialE]^-x^2, 

        D[u[t, x], t] == 0 /. t -> 0, u[t, -x0] == u[t, x0]}], 

      u, {t, 0, x0}, {x, -x0, x0}, 

      Method -> {"MethodOfLines", 

        "SpatialDiscretization" -> {"TensorProductGrid", 

          "DifferenceOrder" -> "Pseudospectral", 

          "MinStepSize" -> 0.2}}]]], {x, -x0, x0}, {t, 0, x0}, 

  MeshFunctions -> {#3 &}, Mesh -> None, ColorFunction -> "Rainbow", 

  PlotPoints -> 20, MaxRecursion -> 1], {{a, 0}, -4, 0}, {{b, 0}, -4, 

  0}, {{c, 1}, -4, 1}, {{d, 0}, -1, 1},

 {{x0, 10, "solution range"}, 5, 20}]
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