2.15.2 Benjamin Bona Mahony \(u_t+u_x + u u+x - u_{xxt} = 0\)

problem number 111

Added December 27, 2018.

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

Solve for \(u(x,t)\)

\[ u_t+u_x + u u+x - u_{xxt} = 0 \]

Mathematica


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

Maple


\[u \left (x , t\right ) = \frac {12 c_{3} c_{2}^{2} \left (\tanh ^{2}\left (c_{3} t +c_{2} x +c_{1}\right )\right )-8 c_{3} c_{2}^{2}-c_{2}-c_{3}}{c_{2}}\]

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