2.15.15 Hunter Saxton \(\left ( u_t + u u_x) \right )_x = \frac {1}{2} (u_x)^2\)

problem number 124

Added December 27, 2018.

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

Hunter Saxton. Solve for \(u(x,t)\) \[ \left ( u_t + u u_x) \right )_x = \frac {1}{2} (u_x)^2 \]

Mathematica


Failed

Maple


\[u \left (x , t\right ) = \frac {2 \RootOf \left (-c_{2} \mathit {\_c}_{1}^{3}-x \mathit {\_c}_{1}^{3}+2 c_{1}^{2} \ln \left (\sqrt {\mathit {\_Z}}\, \mathit {\_c}_{1}+c_{1}\right )+\mathit {\_Z} \mathit {\_c}_{1}^{2}-2 c_{1} \sqrt {\mathit {\_Z}}\, \mathit {\_c}_{1}\right )}{t \mathit {\_c}_{1}+2 c_{3}}\] with RootOf

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