From Mathematica symbolic PDE document.
Korteweg-deVries (waves on shallow water surfaces) with no initial conditions
Solve for \(u(x,t)\) \[ u_{xxx} + u_t -6 u u_x = 0 \] Reference https://en.wikipedia.org/wiki/Korteweg%E2%80%93de_Vries_equation
Mathematica ✓
ClearAll["Global`*"]; pde = D[u[x, t], {x, 3}] + D[u[x, t], {t}] - 6*u[x, t]*D[u[x, t], {x}] == 0; sol = AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
\[\left \{\left \{u(x,t)\to \frac {12 c_1{}^3 \tanh ^2(c_2 t+c_1 x+c_3)-8 c_1{}^3+c_2}{6 c_1}\right \}\right \}\]
Maple ✓
restart; pde := diff(u(x,t),x$3)+ diff(u(x,t),t)-6*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'));
\[u \left (x , t\right ) = 2 c_{2}^{2} \left (\tanh ^{2}\left (c_{3} t +c_{2} x +c_{1}\right )\right )+\frac {-8 c_{2}^{3}+c_{3}}{6 c_{2}}\]