Added December 27, 2018.
Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations
Benjamin Ono. Solve for \(u(x,t)\) \[ u_t+H u_{xx} +u u_x = 0 \] Important note. \(H\) above is meant to be Hilbert transform. https://en.wikipedia.org/wiki/Benjamin%E2%80%93Ono_equation However, here in the code below it is taken as just a scalar. Need to correct this when I have time.
Mathematica ✓
ClearAll["Global`*"]; pde = D[u[x, t], t] + h*D[u[x, t], {x, 2}] + u[x, t]*D[u[x, t], x] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
\[\left \{\left \{u(x,t)\to 2 c_1 h \tanh (c_2 t+c_1 x+c_3)-\frac {c_2}{c_1}\right \}\right \}\]
Maple ✓
restart; pde := diff(u(x,t),t)+H*diff(u(x,t),x$2)+u(x,t)*diff(u(x,t),x)=0; cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
\[u \left ( x,t \right ) ={\frac {2\,H{{\it \_C2}}^{2}\tanh \left ( {\it \_C2}\,x+{\it \_C3}\,t+{\it \_C1} \right ) -{\it \_C3}}{{\it \_C2}}}\]
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