Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
phi equation. Solve for \(phi(x,t)\) \[ \phi _{tt} - \phi _{xx} - \phi + \phi ^3 = 0 \]
Mathematica ✓
ClearAll["Global`*"]; pde = D[phi[x, t], t, t] - D[phi[x, t], x, x] - phi[x, t] + phi[x, t]^3 == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, phi[x, t], {x, t}], 60*10]];
\begin {align*} & \left \{\phi (x,t)\to -\tanh \left (c_2 t-\sqrt {\frac {1}{2}+c_2{}^2} x+c_3\right )\right \}\\& \left \{\phi (x,t)\to \tanh \left (c_2 t-\sqrt {\frac {1}{2}+c_2{}^2} x+c_3\right )\right \}\\& \left \{\phi (x,t)\to -\tanh \left (c_2 t+\sqrt {\frac {1}{2}+c_2{}^2} x+c_3\right )\right \}\\& \left \{\phi (x,t)\to \tanh \left (c_2 t+\sqrt {\frac {1}{2}+c_2{}^2} x+c_3\right )\right \}\\ \end {align*}
Maple ✓
restart; pde := diff(phi(x,t),t$2)-diff(phi(x,t),x$2) - phi(x,t) + phi(x,t)^3=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',PDEtools:-TWSolutions(pde,phi(x,t))),output='realtime'));
\begin {align*} & \{\phi \left (x , t\right ) = -1\}\\& \{\phi \left (x , t\right ) = 1\}\\& \left \{\phi \left (x , t\right ) = -\tanh \left (c_{2} x +c_{1}-\frac {\sqrt {4 c_{2}^{2}-2}\, t}{2}\right )\right \}\\& \left \{\phi \left (x , t\right ) = \tanh \left (c_{2} x +c_{1}+\frac {\sqrt {4 c_{2}^{2}-2}\, t}{2}\right )\right \}\\& \left \{\phi \left (x , t\right ) = \tanh \left (c_{2} x +c_{1}-\frac {\sqrt {4 c_{2}^{2}-2}\, t}{2}\right )\right \}\\& \left \{\phi \left (x , t\right ) = -\tanh \left (c_{2} x +c_{1}+\frac {\sqrt {4 c_{2}^{2}-2}\, t}{2}\right )\right \}\\ \end {align*}