SetDirectory["e:\\data\\demopdespecialsolutions\\\
analyzesolveMarch2010"]

Get["PDESpecialSolutionsV3.m"]

PDESpecialSolutions[{D[u[x, t], t] + D[v[x, t], x]  ==  0,  
        D[v[x, t],  t] + D[u[x, t],  x] - 3*u[x, t]*D[u[x, t], x] - 
            alpha*D[u[x, t], {x, 3}]  ==  0},  {u[x, t], 
        v[x, t]},  {x, t},  {alpha},  Verbose -> True,  
      Form -> Sech,  SymbolicTest -> True]

PDESpecialSolutions[
      D[u[x, y, z, t],  t]  +  6*u[x, y, z, t]^2*D[u[x, y, z, t], x]  +  
          D[u[x, y, z, t], {x, 1}, {y, 1}, {z, 1}]  ==  0,  
      u[x, y, z, t],  {x, y, z, t},  {},  Form -> Sech]

PDESpecialSolutions[{D[u[x, t],  t]  -  D[u[x, t],  x]  -  
            2*v[x, t]  ==  0,  
        D[v[x, t],  t]  +  2*u[x, t]*w[x, t]  ==  0,  
        D[w[x, t],  t]  +  2*u[x, t]*v[x, t]  ==  0},  {u[x, 
          t],  v[x, t],  w[x, t]},  {x, t},  {},  
      Form -> SechTanh]

PDESpecialSolutions[
      D[u[x, y, z, t], t]  +  
alpha*u[x, y, z, t]*
            D[u[x, y, z, t], x]  + 
D[
            u[x, y, z, t],  {x, 3}] + 
D[u[x, y, z, t],  
            y,  y, y]  + 
D[u[x, y, z, t],  z,  z,  
            z]  == 0, 
u[x, y, z, 
        t], 
{x, y, z, 
        t}, 
{alpha}]

PDESpecialSolutions[
      D[u[x, y, z, t], t]  +  
alpha*u[x, y, z, t]*
            D[u[x, y, z, t], x]  + 
D[
            u[x, y, z, t],  {x, 3}] + 
D[u[x, y, z, t],  
            x,  y, y]  + 
D[u[x, y, z, t],  x,  z,  
            z]  == 0, 
u[x, y, z, 
        t], 
{x, y, z, t}, 
{alpha},  
      Form -> Sech]

PDESpecialSolutions[
      D[u[x, y, z, t],  t]  + 
alpha * 
            u[x, y, z, t] ^ 2 * 
            D[u[x, y, z, t], x]  +  
D[
            u[x, y, z, t],  {x, 3}] + 
D[u[x, y, z, t],  
            x,  y, y]  + 
D[u[x, y, z, t],  x,  z,  
            z]  == 0, 
u[x, y, z, 
        t], 
{x, y, z, 
        t}, 
{alpha}]

PDESpecialSolutions[
      D[u[x, y, z, t],  t]  + 
alpha * 
            u[x, y, z, t] ^ 2 * 
            D[u[x, y, z, t], x]  +  
D[
            u[x, y, z, t],  {x, 3}] + 
D[u[x, y, z, t],  
            x,  y, y]  + 
D[u[x, y, z, t],  x,  z,  
            z]  == 0, 
u[x, y, z, 
        t], 
{x, y, z, t}, 
{alpha},  
      Form -> Sech]

PDESpecialSolutions[
D[u[x, t], 
            t]  +  
u[x, t]* 
            D[u[x, t], x]  +  
D[
            u[x, t], {x, 2}] + 
alpha* 
            D[u[x, t], {x, 3}]  +  
D[
            u[x, t], {x, 4}]  ==  0, 
u[x, 
        t], 
{x, t}, 
{alpha},  
      Verbose -> True]

PDESpecialSolutions[{
D[u[x, t], 
              t]  - 
alpha * (6 * u[x, t] * 
                    D[u[x, t], x]   +   D[
                    u[x, t],  {x, 3}])  + 
2 * 
              beta * v[x, t]* D[v[x, t],  x]   == 
          0, 
D[v[x, t], t]  +  
3*
              u[x, t]*D[v[x, t], x]  + 
D[
              v[x, t], {x, 3}]  ==  
          0
}, 
{u[x, t],  v[x, t]}, {x, 
        t}, {alpha,  beta},  Form -> Cn]

PDESpecialSolutions[{
D[u[x, t], 
              t]  +  
 
            alpha * v[x, t]*D[v[x, t], x]  +  
beta*
              u[x, t]*D[u[x, t], x]  + 
gamma * 
              D[u[x, t], {x, 3}]  == 
          0, 
D[v[x, t], t]  +  
delta*
              D[u[x, t]*v[x, t], x]  + 
epsilon*v[x, t]*
              D[v[x, t], x]  == 
          0
}, 
{u[x, t],  
        v[x, t]}, 
{x, t}, 
{alpha,  
        beta,  gamma,  delta, epsilon},  
Form -> 
        Sech]

PDESpecialSolutions[{
D[u[x, t], 
              t]  - 
D[
              u[x, t], {x, 2}]  - 
u[x, 
                t]*(1 - u[x, t])  ==  
          0
}, 
{u[x, t]}, {x, 
        t}, {}]

PDESpecialSolutions[{
beta*
              D[v[z], z]  +  
Sqrt[2]*
              D[v[z],  {z, 2}]  - 
Sqrt[2]*
              v[z]*(1 - Sqrt[2]*v[z])*(alpha - 
                  Sqrt[2]*v[z])  ==  
          0
}, 
{v[
          z]}, 
{z}, 
{alpha,  
        beta}]

PDESpecialSolutions[{
D[u[x, t], 
              t]  - 
D[u[x, t], 
              x]  - 
2*v[x, t]  ==  
          0, 
D[v[x, t], t]  - 
2*
              epsilon*u[x, t]*v[x, t]  == 
          0
}, 
{u[x, t], v[x, t]}, {x, 
        t}, {epsilon}]

PDESpecialSolutions[
      D[u[x, t], t]  + 
6*alpha*u[x, t]*
            D[u[x, t], x]  + 
6*beta*u[x, t]^2*
            D[u[x, t], x]  + 
gamma*
            D[u[x, t],  {x, 3}]  == 0, 
u[x, 
        t], {x, t}, {alpha,  beta,  gamma}]

PDESpecialSolutions[
      D[u[x, t], t]  + 
6*alpha*u[x, t]*
            D[u[x, t], x]  + 
6*beta*u[x, t]^2*
            D[u[x, t], x]  + 
gamma*
            D[u[x, t],  {x, 3}]  == 0, 
u[x, 
        t], {x, t}, {alpha,  beta,  gamma},  Form -> Sech]

PDESpecialSolutions[
      D[u[x, t], t] + alpha*u[x, t]*D[u[x, t], x]  +  
          D[u[x, t],  {x, 3}]  ==  0,  u[x, t],  {x, t},  
      alpha,  Form -> Sech]

PDESpecialSolutions[{D[u[x, t], t] + alpha*u[x, t]*D[u[x, t], x] + 
            D[u[x, t], {x, 2}] == 0},  u[x, t], {x, t}, alpha,  
      Form -> sechtanh]

PDESpecialSolutions[{D[u[x, t], t] + alpha*u[x, t]*D[u[x, t], x] + 
            D[u[x, t], {x, 3}] == 0},  u[x, t], {x, t}, {alpha}, 
      Form -> Cn,  Verbose -> True,  
      NumericTest  ->  True,  
      SymbolicTest  ->  True]

PDESpecialSolutions[{D[u[x, t], t] + alpha*u[x, t]*D[u[x, t], x] + 
            D[u[x, t], {x, 3}] == 0},  u[x, t], {x, t}, {alpha}, 
      Form -> Sn]

PDESpecialSolutions[{D[u[x], {x, 2}] + u[x] + alpha*u[x]^3 == 
          0},  u[x], {x}, {alpha},  Form -> JacobiCN,  
      Verbose  ->  True]

PDESpecialSolutions[{D[u[x], {x, 2}] + u[x] + alpha*u[x]^3 == 
          0},  u[x], {x}, {alpha},  Form -> Sn]

PDESpecialSolutions[{
D[u[x, t], 
              t]  - 
alpha * (6 * u[x, t] * 
                    D[u[x, t], x]   +   D[
                    u[x, t],  {x, 3}])  + 
2 * 
              beta * v[x, t]* D[v[x, t],  x]   == 
          0, 
D[v[x, t], t]  +  
3*
              u[x, t]*D[v[x, t], x]  + 
D[
              v[x, t], {x, 3}]  ==  
          0
}, 
{u[x, t],  v[x, t]}, {x, 
        t}, {alpha,  beta},  Form -> Cn,  NumericTest -> True,  
      Verbose -> True]