Welcome to the Painleve Test Package for Mathematica 4.0:
By Douglas Baldwin and Willy Hereman
© 2000, Colorado School of Mines, Golden CO, 80401

SetDirectory["c:\\painleve\\9-09-00\\painleve"]

<< painleve.m

?PainleveTest

PainleveTest[{D[u[x, t], {x, 2}] + c*D[u[x, t], x] - u[x, t]^2 + 
            u[x, t] == 0}, u[x, t], {x, t}, 
      Kruskal -> x]

PainleveTest[{a[t]*D[u[x, t],  x] + D[u[x, t],  {x,  4}] + 
          6*u[x, t]*D[u[x, t],  {x,  2}] + 6*D[u[x, t],  x]^2 + 
          D[u[x, t],  {x,  1},  {t,  1}]},  
      u[x, t],  {x, t}]

PainleveTest[{D[u[x, t],  t] + u[x, t]*D[u[x, t],  x] - 
          sigma*D[u[x, t],  {x, 2}]},  u[x, t],  {x, t}]

PainleveTest[{D[u[x, t],  t] +  6*u[x, t]*D[u[x, t],  x] + 
          D[u[x, t],  {x, 3}]},  u[x, t],  {x, t},  
      Kruskal -> x]

PainleveTest[{D[u[x, t],  t] - 3* u[x, t]^2*D[u[x, t],  x] + 
          2*sigma^2*D[u[x, t],  {x, 3}]}, u[x, t],  {x, t}]

PainleveTest[{D[u[x, t],  {t, 2}] + 2*u[x, t]*D[u[x, t],  {x, 2}] + 
          2*D[u[x, t],  x]^2 + (1/3)*D[u[x, t],  {x, 4}]},  
      u[x, t],  {x, t}]

PainleveTest[{u[x, 
              t]*(D[u[x, t],  {t,  2}] - D[u[x, t],  {x, 2}]) - 
          D[u[x, t],  t]^2 + 
          D[u[x, t],  x]^2  -  (1/2)*u[x, t]^3 + (1/2)*u[x, t]},  
      u[x, t],  {x, t}]

PainleveTest[{-2*D[u[x, t],  t]*D[u[x, t],  x] + 
          2*u[x, t]*D[u[x, t],  {x,  1},  {t,  1}] - u[x, t]^3 + 
          u[x, t]}, u[x, t],  {x, t}]

PainleveTest[{u[x, 
              t]*(D[u[x, t],  {t,  2}] - D[u[x, t],  {x, 2}]) - 
          D[u[x, t],  t]^2 + D[u[x, t],  x]^2  -  u[x, t]^3},  
      u[x, t],  {x, t}]

PainleveTest[{2*u[x, t]*D[u[x, t],  t] + D[u[x, t],  {x,  2}]}, 
      u[x, t],  {x, t}]

PainleveTest[{D[u[x, t],  t] + D[v[x, t],  {x, 2}] + 
          a*v[x, t]*(u[x, t]^2 + v[x, t]^2),  
        D[v[x, t],  t] - D[u[x, t],  {x, 2}] - 
          a*u[x, t]*(u[x, t]^2 + v[x, t]^2)},  {u[x, t],  
        v[x, t]},  {x, t},  Kruskal -> x]

PainleveTest[{D[u[x, t], x] + mu*v[x, t],  
        D[v[x, t],  x] - e[x, t]*w[x, t] - mu*u[x, t],  
        D[w[x, t],  x] + e[x, t]*v[x, t],  
        D[e[x, t],  t] + v[x, t]},  {u[x, t], v[x, t], w[x, t], 
        e[x, t]}, {x, t}, Kruskal -> x]

PainleveTest[{v[x, t] - D[u[x, t],  t],  
        u[x, t] - u[x, t]*w[x, t] - D[v[x, t],  t],  
        u[x, t]*v[x, t] - D[w[x, t],  t]},  {u[x, t],  v[x, t], 
        w[x, t]},  {x, t}, Kruskal -> x]

(* 
      Nonlinearly coupled interacting harmonic oscillators. *)

PainleveTest[{D[u[x, t],  {t,  2}] + w1^2*u[x, t]  +  
          mu*v[x, t]*w[x, t],  
        D[v[x, t],  {t,  2}] + w1^2*v[x, t]  +  mu*u[x, t]*w[x, t],  
        D[w[x, t],  {t,  2}] + w1^2*w[x, t]  +  mu*u[x, t]*v[x, t]},  {u[
          x, t],  v[x, t],  w[x, t]},  {x, t}]

PainleveTest[{-D[u[x, t],  
              t] + (1/
                3)*(-D[u[x, t],  {x,  2}] - (7/2)*
                  D[u[x, t],  x]*v[x, t] + (1/2)*u[x, t]*
                  D[v[x, t],  x] - u[x, t]^2*v[x, t]),  -D[
              v[x, t], {t,  2}] + 
          D[v[x, t],  {x,  2}] - (1/2)*D[u[x, t],  x]*
            v[x, t] + (3/2)*u[x, t]*D[v[x, t],  x]},  {u[x, t],  
        v[x, t]},  {x, t}]

PainleveTest[{-aa*D[u[x, t],  {x,  3}] - 
          6*aa*u[x, t]*D[u[x, t],  x] + 6*v[x, t]*D[v[x, t],  x] + 
          D[u[x, t],  t], 
D[v[x, t],  {x,  3}] + 
          3*u[x, t]*D[v[x, t],  x] + D[v[x, t],  t]},  {u[x, t], 
        v[x, t]},  {x, t},  Kruskal -> x]