#### 2.15.3 Benjamin Ono $$u_t+H u_{xx} +u u_x = 0$$

problem number 112

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

$\left \{\left \{u(x,t)\to 2 c_1 h \tanh (c_2 t+c_1 x+c_3)-\frac {c_2}{c_1}\right \}\right \}$

Maple

$u \left (x , t\right ) = \frac {2 H c_{2}^{2} \tanh \left (c_{3} t +c_{2} x +c_{1}\right )-c_{3}}{c_{2}}$

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