2.15.2 Benjamin Bona Mahony $u_t+u_x+uu+x-u_{xxt}=0$

problem number 112

Added December 27, 2018.

Taken from https://en.wikipedia.org/wiki/List_of_nonlinear_partial_differential_equations

Solve for $u(x,t)$

$$u_t+u_x+uu+x-u_{xxt}=0$$

Mathematica ✓

ClearAll["Global`*"]; 
pde =  D[u[x, t], t] + D[u[x, t], x] + u[x, t]*D[u[x, t], x] - D[D[u[x, t], {x, 2}], t] == 0; 
sol =  AbsoluteTiming[TimeConstrained[DSolve[pde, u[x, t], {x, t}], 60*10]];
 

$$\left\{\{u(x,t)\to 12c_1{c}_2{\tanh }^2(c_{2}t+c_{1}x+c_3)-8c_1{c}_2-\frac{c_2}{c_1}-1\}\right\}$$

Maple ✓

restart; 
pde := diff(u(x,t),t)+diff(u(x,t),x)+u(x,t)*diff(u(x,t),x)-diff(u(x,t),x,x,t)=0; 
cpu_time := timelimit(60*10,CodeTools[Usage](assign('sol',pdsolve(pde,u(x,t))),output='realtime'));
 

$$u(x,t)=\frac{12\mathit{\_}\mathit{C}\mathit{3}{\mathit{\_}\mathit{C}\mathit{2}}^2{(\tanh (\mathit{\_}\mathit{C}\mathit{2}x+\mathit{\_}\mathit{C}\mathit{3}t+\mathit{\_}\mathit{C}\mathit{1}))}^2-8{\mathit{\_}\mathit{C}\mathit{2}}^2\mathit{\_}\mathit{C}\mathit{3}-\mathit{\_}\mathit{C}\mathit{2}-\mathit{\_}\mathit{C}\mathit{3}}{\mathit{\_}\mathit{C}\mathit{2}}$$

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