2.15.1 Bateman-Burgers \(u_t+u u_x = \nu u_{xx}\)

problem number 110

Added December 27, 2018.

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

Bateman-Burgers.

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

\[ u_t+u u_x = \nu u_{xx} \]

Mathematica


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

Maple


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

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